Research Article Sleeping Schedule-Aware Local Broadcast...

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 451970 10 pageshttpdxdoiorg1011552013451970

Research ArticleSleeping Schedule-Aware Local Broadcast inWireless Sensor Networks

Jue Hong1 Zhuo Li23 Dianjie Lu4 and Sanglu Lu3

1 Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen Guangdong 518055 China2 Beijing Key Lab of Internet Culture and Digital Dissemination Research Beijing Information Science amp Technology UniversityBeijing 100101 China

3 State Key Lab of Novel Software Technology Nanjing University Nanjing Jiangsu 210023 China4 School of Information Science and Engineering Shandong Normal University Jinan Shandong 250014 China

Correspondence should be addressed to Zhuo Li lizhuobistueducn

Received 23 August 2013 Accepted 8 November 2013

Academic Editor Ming Liu

Copyright copy 2013 Jue Hong et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Broadcast is widely used in applications in wireless sensor networks (WSNs) In the last decade the broadcast problem inWSNs hasbeen well studied However few of existing broadcasting strategies have considered the scenarios with sleeping schedules whichhave been emerging as a prevalent energy-savingmethod forWSNs InWSNswith sleeping schedule each node switches on and offperiodically rendering the broadcast problem more difficult To handle the periodical sleep issue we focus on designing effectivesleeping schedule-aware broadcast algorithms We practically propose SALB a sleeping schedule-aware local broadcast algorithmIn SALB a typical local algorithm for constructing connected dominating set is employed to form the broadcast backbone Toguarantee proper transmission of broadcast messages a sleep-aware forwarding mechanism is implemented Moreover heuristicstrategies are used to decrease the number of transmissions and the broadcast latency Theoretical analysis shows that the numberof transmissions for SALB is within 4(min(Δ|119879|) + 119888) (119888 is constant) is constant) times of the optimal value And the broadcastlatency of SALB is within 4|119879| +1 times of the optimal value (Δ is the maximum degree in the network |119879| is the scheduling periodlength) The performance of SALB is evaluated via simulations

1 Introduction

Energy is regarded as scarce resource in wireless sensornetworks (WSNs) It is shown that most energy is wastedin sensor nodersquos idle listening To handle this issue sleepingschedule has been proposed to preserve energy in WSNsWith sleeping schedule each node is switched on and offperiodically Nodes turn on to detect object and receive andforward data and then turn to sleep to save energy As a simpleyet efficient method sleeping scheduling has been widelyused in WSN applications like environment monitoring andobject tracking applications [1]

Broadcast is a fundamental operation in WSNs forrouting discovery information dissemination and so on[2] Naive broadcast methods such as flooding always lead

to massive redundancy and intolerable latency wasting theenergy dramatically [2] In order to design energy-efficientbroadcast algorithms a lot of effort has been devoted toreduce data transmission and broadcast latency For instancemany MCDS-based approaches are proposed to minimizetransmission redundancy [3ndash7] And lots of coloring-basedcollision-avoiding approaches are used to reduce latency [8ndash10]

In this paper we focus on the sleeping schedule-warebroadcast problem in WSNs which is quite different fromthat in traditional WSNs In traditional WSNs each node isassumed to be nonsleeping Based on the broadcast nature ofwireless medium a node can deliver one broadcast messageto all its neighbors by one transmission While in the WSNswith sleeping schedule each node can only receive messages

2 International Journal of Distributed Sensor Networks

when it is active so not all neighbors of a senor node canreceive the broadcast message by one transmission This dif-ference renders the broadcast problem more difficult in suchsituations Existing broadcast algorithms did not consider thesleeping schedule issues and thus are not suitable

To solve the sleeping schedule-aware broadcast problemwe practically propose a local algorithm in this papernamely the sleeping schedule-aware local broadcast (SALB)algorithm In SALB we first use a typical local MCDSconstruction algorithm to form a virtual broadcast backboneWith this virtual backbone we design an active slot-basedforwarding mechanism for each node which guaranteesthe success of broadcast and can help reduce transmissionredundancy and latency The numbers of transmissions forSALB are within 4(min(Δ |119879|)+119888) (c is constant) times of theoptimal value And the broadcast latency of SALB is within4|119879| + 1 times of the minimum value (Δ is the maximumdegree in the network |119879| is the scheduling period length)

The rest of this paper is organized as follows We reviewthe related work in Section 2 and present the models andassumption in Section 3 SALB is proposed in Section 4 Weevaluate its performance in Section 5 and discuss the tradeoffbetween the number of transmissions and the broadcastlatency in Section 6 In Section 7 we conclude this paper

2 Related Work

Data-transmission issues in duty-cycled WANETs haverecently attractedmuch of researchersrsquo attentionDousse et al[11] established a bound on the transmission latency of sensornetworks with uncoordinated schedule Lu et al provedthe NP-hardness of minimizing end-to-end communicationdelay in low-duty-cycle sensor networks in [12] Cao etal proposed the pipeline forwarding pattern for sensornetworks with a sleeping schedule to decrease the delay [13]Keshavarzian et al analyzed the delay of several knownwake-up patterns and proposed a new multiparent schedulingpattern for sensor networks in [14] Gu and He proposeda dynamic data forwarding scheme for extremely low-duty-cycle sensor networks based on the expected latency andreliability model [15] However these works mainly focus onthe latency issue caused by the sleep schedule and none ofthem refer to the broadcast problem

Since broadcast plays an important role in WSNs a lotof research work has been done on this area The simplestapproach for broadcast is blind flooding where each node isobligated to forward a packet upon receiving it for the firsttime However it has been shown that blind flooding can leadto serious redundancy and collisions a situation known asbroadcast storm [2] Therefore great effort has been madeby improving the flooding approach to reduce broadcastredundancy and collisions as well as broadcast latency Forexample [2 16] proposed probabilistic forwarding methodsto avoid massive redundant transmissions Based on theconstruction of virtual broadcast backbone and broadcastingalong the backbone [3ndash7] proposed different technologiesto reduce broadcast redundancy Specifically much recentresearch has been done to minimize the broadcast transmis-sions and minimize the broadcast latency based on different

Table 1 Notations

119899 The number of nodes in the network119879 The period of sleeping scheduleΔ Themaximum degree of nodes in the network119873(V) The set of neighbors of node V119863(V) The set of 1-hop neighbor dominators of node V1198632(V) The set of 2-hop neighbor dominators of node V

SL119886(V) The active time-slot of node V

network models Generally both the minimum transmissionbroadcast problem and the minimum latency broadcastproblem are NP-hard and a lot of efficient algorithms havebeen proposed [3ndash10]

Recently some researches focusing on the sleepingschedule-aware broadcast problem have emerged Wang etal discussed the broadcast problem in duty-cycle sensornetworks in [17] Hong et al proposed a series of workon the minimum-redundancy broadcast problem for duty-cycle wireless ad hoc networks [18 19] The other topic ofminimum-latency broadcast problem has been investigatedin [20 21] However none of them proposes a local algo-rithm for sensor network considering both transmission andlatency issues of broadcast

3 Model and Assumption

We assume that 119899 sensors node are deployed in a two-dimensional plane with equal maximum transmitting rangeof one unitThenetwork can bemodeled as a connectedUDG119866(119881 119864) where 119881 is the set of nodes and 119864 is the edge set Anedge 119906 V isin 119864 if and only if the distance between nodes uand v is within each otherrsquos communication range Unlike theliterature focusing on tuning sleeping schedule [12ndash14] wefollow the assumption in [11] where each node determinesits sleeping schedule completely and uncoordinatedly Weassume that the scheduling period 119879 is divided into|119879|time-slots with fixed and equal length denoted by 1 2 |119879|

accordingly We also assume that each node v randomlychooses an active time-slot SL

119886(V) isin 119879 independently Each

time-slot is assumed to be long enough for sending orreceiving a data packet [12] The contention and collisionissues of wireless channel are assumed to process by theMACprotocols for example S-MAC [22] Therefore we will notneed to consider the impact of factors like channel conflictFollowing the models in [12 15] we assume that a node canwake up to transmit at any time but can receive only inits active time-slot The set of sending time-slots of node Vis SL119904(V) The global time synchronization is guaranteed by

protocols like flooding time synchronization protocol (FTSP)[23]

The notations used in this paper are listed in Table 1

31 Problem Formulation We consider the multisourcebroadcast in this paper in which each node in the network ispossible to broadcast the data packets to all the other nodesIn the general WSN with the benefit of broadcasting nature

International Journal of Distributed Sensor Networks 3

of wireless media each node can broadcast the data packetsto all neighbor nodes with only one transmission As a resultthe objective of traditional broadcasting algorithm is to deter-mine the forwarding nodes in broadcasting Each forwardingnode retransmits the data packets once after receiving themto complete the broadcasting process However consideringthe effect of sleeping schedule the active time-slots of nodesare always different A node cannot guarantee that all itsneighbors are able to receive the data package successfullywith one transmission As a result the broadcasting problembecomes different from the traditional WSN and thus isneeded to be redefinedWedefine a broadcast backbone 119861(119866)

on 119866(119881 119864) as a subset of V where the broadcast backboneis the set of forwarding nodes The data package will beforwarded in the network on the broadcasting backboneAlsowe define a broadcast schedule BS(B) as the set of SL

119904(V) in

which v is the node in broadcasting backbone B We alsodefine Cov

119894(V) as the set of neighbor nodes in which node

v covers at time-slot iThe sleeping schedule-aware broadcastproblem can be described as follows

Definition 1 (the sleeping schedule-aware broadcast (SA-broadcast)) Given a WSN with sleeping schedule which ismodeled as a UDG 119866(119881 119864) find a connected backbone 119861(119866)for broadcast and a corresponding broadcast schedule BS(119861)so that⋃Visin119861(⋃119894isinSL

119904(V) COV119894(V)) = 119881

Different broadcasting algorithms have different broad-cast backbones and broadcast schedules which determine thenumber of transmissions and the broadcast latency Finallywe present a useful definition

Definition 2 (inversion) Given a data transmitting nodesequence V

0 V1 V

119896 V119896+1

for two adjacent transmittingand receiving nodes V

119896and V119896+1

if SL119886(V119896) le SL

119886(V119896+1

) holdswe define it as an inversion

When node 119886 receives a data package at time-slot SL119886(119886)

and sends data to node c through node b if there is noinversion node c can receive the data package within theminimum latency SL

119886(119888) minus SL

119886(119886) time-slots If an inversion

exists for example SL119886(119886) ge SL

119886(119887) the latency of node

c receiving the data package will be increased by |119879| time-slots If the inversion appears k times the time-slots willbe increased by 119896|119879| Therefore to decrease the latency weusually try to avoid the appearance of inversions in thesequence of forwarding nodes from the source node to thedestination node

4 Local Algorithm for SA-Broadcast Problem

In this section we introduce the details of the proposed SALBalgorithm The design of SALB algorithm consists of twoparts construction of a broadcast backbone and the activetime-slot-oriented forwarding mechanism

41 Construction of Broadcast Backbone Among existingbroadcast backbone constructing algorithms the MCDS is

proved to have the minimum forwarding nodes perform-ing well in reducing both transmission and latency [24]Therefore we would like to use a MCDS as the broadcastbackbone Many MCDS constructing algorithms have beenproposed so far like [25ndash28] Among them a widely usedlocal algorithm for mobile ad hoc networks proposed byAlzoubi et al in [25] has constant message complexity andconstant approximation ratio Therefore we employ thisalgorithm with some modification here to construct thebroadcast backbone of SALB

As described in [7 25] the construction of broadcastbackbone can consist of two phases dominator electionand dominator connection The elected dominators andconnectors form a connected dominating set (CDS) actingas the broadcast backbone In the construction phase of thebroadcast backbone we assume that all nodes are in theactive state After the construction each node will becomea dominator a dominate or a connector According to [25]there must be a dominator within three hop distance of anydominator During the broadcast each dominator deliversmessage to its neighbors and connectors relay messagesamong dominators Each node maintains a forwarding nodelist FWD LIST containing the IDs of destination nodesand their active time-slots The FWD LIST will be used indesigning the forwarding mechanism

411 Electing Dominators We assume that each node in thenetwork obtains all its 1-hop neighborsrsquo ID and active time-slot by exchanging beacon messages To reduce inversions inthe broadcast process we would like to make the active time-slot of each dominator smaller than its neighborsrsquo Let 119873(V)be the set of node Vrsquos 1-hop neighbors We define a metric 120578to represent the possibility of no inversion happening while anode 119906 transmits to its neighbors

120578 =

1003816100381610038161003816119906 | 119906 isin 119873 (V) SL119886(V) lt SL

119886(119906)

1003816100381610038161003816

|119873 (V)| (1)

In electing the dominators nodes with larger value of 120578 willbe more likely to win Initially all nodes are in the ldquoBlankrdquostate Then the modified election procedure based on that in[25] with metric 120578 is as follows

(i) A Blank node becomes a dominator if it has thelargest 120578 among all its Blank 1-hop neighbors and thenbroadcast amessage IamDominator (ID i) with its IDand active time-lot i (ID is used to break the tie)

(ii) A Blank node becomes a dominator if there are noBlank nodes nor dominators in its 1-hop neighbors(knowledge from the received IamDominatee mes-sage) and then broadcast the IamDominator(ID i)message

(iii) A Blank node becomes a dominatee if it receives aIamDominator message and then broadcast messageIamDominatee(ID i)

After election if a dominator 119906 has the largest ID amongall its dominatee Vrsquos neighbor dominators it stores the ID andthe schedule of active time-slots of V in its FWD LIST Each


Choosing 1-hop connectors for dominator(1) If 119879119890119898119901 == 0 then stop else execute the following steps(2) For each dominatee in HOP1 LIST compute the number 119899 of dominators in 119879119890119898119901(3) Choose the dominatee with largest 119899 as 1-hop connector(4) Remove the item of V from the HOP1 LIST and remove all dominators connected byV from 119879119890119898119901 go to Step 1

Algorithm 1

Choosing 1-hop connectors for dominatee(1) Find V1015840 from the SPCON LIST which connects to most isolated dominators in 119879119890119898119901(2) Mark V1015840 as an 1-hop connector and removes all nodes it connects to from 119879119890119898119901(3) Store V1015840rsquos ID and active time-slot in FWD LIST(4) Go to Step 1 until 119879119890119898119901 == 0

Algorithm 2

dominatee then records all of its dominatorrsquos IDs and activetime-slots in its FWD LIST

412 Connecting Dominators Here we present the modifieddominator connecting phase based on the algorithm from[25] For each dominator we call the connecting nodesadjacent to its 2-hop dominators the 1-hop connectors andthe connecting nodes 2-hop away from its 3-hop dominatorsthe 2-hop connectors

First we connect dominators with its 2-hop neighbordominators After the election phase each dominatee Vbroadcasts an ANNOUNCE message containing the IDs ofnodes in 119863(V) Hence each dominator 119906 is able to obtainthe set of all its 2-hop dominators 119863

2(119906) and the dominatees

through which the nodes in 1198632(119906) can be reached Domina-

tor 119906 keeps this information in a list HOP1 LISTV 119863(V) cup1198632(119906) and uses a working set 119879119890119898119901 = 119863

2(119906) for the

1-hop connector selection Dominator 119906 then broadcastsan ANNOUNCE message containing the IDs of all nodesin 1198632(119906) so that all dominatees in 119873(119906) can obtain the

information of 119906rsquos 2-hop neighbor dominators If dominator119906 does not have the largest ID among its dominatee Vrsquos 1-hop dominators V will not be chosen as 119906rsquos 1-hop connectorsAnd the item of V will be removed from 119906rsquos HOP1 LIST andall Vrsquos 1-hop dominators will be removed from 119879119890119898119901 Afterthe removal dominator 119906 chooses 1-hop connectors for its 2-hop dominators using the procedure shown in Algorithm 1

After choosing its 1-hop connector each dominator putsthe ID of its 1-hop connectors and the connected dominatorsin 119879119890119898119901 in a HOP1 CONN message and then broadcast Ifa dominatee receives a HOP1 CONN message and finds itsID included it marks itself as a connector and adds the IDand active time-slots of nodes attached in the HOP1 CONNmessage into its FWD LIST

Next we connect the dominator and its 3-hop neighbordominators After a dominator 119906 broadcasts the IDs of allnodes in 119863

2(119906) with the ANNOUNCE message its domi-

natee V is able to gather the information of 2-hop neighbor

dominators of 119906Then V puts its 1-hop and 2-hop dominatorsrsquoinformation in an ANNOUNCE message and broadcastWhen dominator 119906 receives all the ANNOUNCE messagesbroadcasted by its dominatees it is able to know the 2-hopneighbor dominators 119863

2(119908) for each dominator 119908 in 119863

2(119906)

which will then be stored in a list When a dominatee Vreceives the ANNOUNCE message from other dominateesit checks their dominators If there is some dominatee 119909

which does not share 1-hop dominators with V V will mark119909 as a special dominatee and mark its corresponding dom-inators as special dominators Dominatee V maintains a listSPCON LIST to store the special dominators for each specialdominatees and then broadcast them with an ANNOUNCEmessage

When dominator 119906 receives theANNOUNCE fromdom-inatee V it checks the special dominators inside the messageIf there are nodes in the message which are neither 2-hopneighbor dominators of 119906 nor the special dominators forthe 2-hop neighbor dominators of any node in 119863

2(119906) 119906 will

mark them as isolated dominators If a dominatee V satisfiesthe following conditions (1) there are isolated dominatorsmarked by 119906 in Vrsquos dominators and (2) 119906 owns the largest IDamong all isolated dominators and Vrsquos dominators [25] 119906willchoose V as a 2-hop connector and notify V with the isolateddominators it needs to connect to Receiving the messagefrom 119906 dominatee V fetches the isolated dominators it needsto connect to and store them in 119879119890119898119901 After that it finds thecorresponding 1-hop connectors using the procedure shownin Algorithm 2

After that each 2-hop connector stores the informationof its isolated dominators in HOP1 CONN message anddelivers the message to its 1-hop connectors When these 1-hop connectors receive the message they store the ID as wellas the active time-slots of the source 2-hop connectors and theisolated dominators they needs to connect to in FWD LIST

42 Active Time-Slot-Oriented Forwarding Mechanism In aconventional WSN broadcast can be finished if each node


The forwarding mechanism for node v when receiving a broadcast packet(1) If the packet is not received for the first time then it is just dropped and the following stepsare skipped According to the ID and SEQ of the packet(2) Let 119879119890119898119901 be the set of nodes in the FWD LIST excluding the one where the packet was justfrom(3) 119905 = (SL

119886(V) + 1)119898119900119889 |119879|

(4) If exist119906 isin 119879119890119898119901 and SL119886(119906) == 119905 then broadcast the packet at time slot 119905

(5) For each node 119906 isin 119879119890119898119901 if SL119886(119906) == 119905 then delete 119906 from 119879119890119898119901

(6) If 119879119890119898119901 == 0 then stop forwarding otherwise let 119905 = (119905 + 1)119898119900119889 |119879| and go to Step 4

Algorithm 3

in the broadcast backbone forwards the packet to all itsneighbor nodes only once receiving a packet However in anetwork with sleeping schedule nodes have to forward thepacket according to the schedule of active time-slots of allits receivers Therefore to execute the broadcast operationcorrectly we have to design the forwarding mechanism fornodes in the broadcast backbone that is broadcast scheduleTo distinguish the packets from the same source node ordifferent source nodes each broadcast packet includes the IDof its source node as well as an increasing sequence numberSEQ which is maintained by the source node Based on theFWD LIST list kept by each node the forwardingmechanismfor a node when receiving a broadcast packet is shown inAlgorithm 3

When a connector or dominator node 119904 starts a broadcastoperation it keeps 119879119890119898119901 as the set of all nodes in theFWD LIST and starts the forwarding process as in step (3)If 119904 is a dominatee it forwards the packet to some adjacentdominator directly From the above forwarding mechanismwe can see that nodes do not send the packet to the nodes inthe FWD LIST one by one but forward according to theiractive time-slots Therefore the numbers of transmissionsare greatly reduced because an effective transmission cancover all active neighbors in the corresponding time-slotMeanwhile a node starts the forwarding process once itreceives a packet such that following up active neighbornodes can receive the packet as soon as possible reducing thebroadcast latency

5 Performance Evaluation

In this section we first present theoretical analysis of thetransmission number broadcast latency and the complexityof SALB Then we conduct simulations to evaluate theperformance of SALB

51 Theoretical Analysis Since the broadcast virtual back-bone of SALB is a CDS if each node in the virtual backbonesucceeds in delivering broadcast messages to its neighbornodes all nodes in the network are guaranteed to receivethe broadcast message Based on this fact with the activeslot-based forwarding mechanism SALB obviously providescorrect broadcasting operation Next we give two theoremson broadcast transmission and latency of SALB

Assuming the minimum number of transmission tocomplete a broadcast in the network is 119877min we have thefollowing

Theorem 3 The numbers of transmissions of SALB arebounded by (min(Δ |119879| + 119888))(4119877min + 1) where c is constant

Proof Assume that the WSN is modeled as a UDG 119866(119881 119864)According Lemma 1 in [7] the dominating set 119878 elected in thevirtual backbonersquos constructing phase of SALB is a maximalindependent set of119866 During the broadcasting of SALB eachdominator in 119878 will transmit the message to nodes in itsFWD LIST For each dominator 119906 the nodes in FWD LISTare a subset of119873(119906) Since the transmission of node 119906 is onlyaccording to the schedule of the active slots of nodes in119873(119906)the number of necessary transmissions is at mostmin(Δ |119879|)To cover its 2-hop neighbor dominators the 1-hop connectorsof node 119906 need at most 119897

2transmission totally where 119897

2is

the number of node 119906rsquos 2-hop neighbor dominators Alsothe 2-hop connector of node 119906 will need to transmit messageto node 119906rsquos 3-hop neighbor dominators through their 1-hopconnectors respectively Denoting the number of node 119906rsquos 3-hop neighbor dominators as 119897

3 the numbers of transmissions

to cover all 3-hop neighbor dominators of node 119906 are at most21198973because each 3-hop dominator connects to only one 1-

hop connector in the worst case Therefore the numbers oftransmissions119872 to finish the broadcast equal |119878|(min(Δ |119879|+1198972+ 21198973))

Let the size of MCDS of 119866 be MCDS according toLemma 2 in [25] we have |119878| le 4MCDS+1 And accordingto Lemma 2 in [28] both 119897

2and 1198973are bounded by constants

in a UDG Hence we use a constant 119888 to denote the upperbound of 119897

2+ 21198973 On the other hand in any WSN which

can be modeled as a UDG the minimum transmission119877min of broadcast is obviously has lower bound MCDSSummarizing all above we have

119872 = |119878| (min (Δ |119879|) + 1198972+ 21198973)

le (min (Δ |119879|) + 119888) (4MCDS + 1)

le (min (Δ |119879|) + 119888) (4119877min + 1)

(2)

The theorem holds


middot middot middot

middot middot middotd0 d1 d2 dn

unu0 u1 u2

a0 a1 a2 a3

Figure 1 Latency analysis of SALB

Theorem 3 shows that in situations with sparse nodedensity or short sleeping scheduling period the broadcasttransmission of SALB will be closer to the optimal value

Next we analyze the broadcast latency of SALB Denotingthe minimum broadcast latency in a WSN with sleepingschedule by 119871min we have the following

Theorem 4 The broadcast latency of SALB is bounded by(4|119879| + 1)119871min

Proof Denote the virtual broadcast backbone constructed inSALB by 119861 119861 is a connected dominating set of the UDG 119866

corresponding to theWSN By adding edges connecting eachdominator and its dominatees in 119861 we obtain a new graph1198611015840 According to Lemma 5 in [28] the hop-distance between

any two nodes 119906 and V in 1198611015840 is less or equal to three times

of the minimum distance between them in 119866 As shown inFigure 1 assume that the path with minimum distance in 119866

between nodes 119906 and V is 119901119866(1199060 119906119899) = 119906

01199061sdot sdot sdot 119906119899 where

119906 = 1199060 V = 119906

119899 If 119906119894is a dominator let119889

119894be its dominatee If 119906

119894

is a dominatee let 119889119894= 119906119894 It is obvious that there exists a path

119889119894119906119894119906119894+1

119889119894+1

in119866 According to the connecting phase in SALBat most two nodes are needed to connect two nodes 119889

119894and

119889119894+1

Therefore nodes 1199060and 119906119899can be connected with a path

1199011198611015840(1199060 119906119899) = 11990601198890119886011988611198891119886211988631198892sdot sdot sdot 119889119899119906119899in graph 119861

1015840 where1198860 1198861 are connecting nodes in 119861 If the minimum hop-

distance between 119906 and V is 119899 in graph 119866 then the maximumdistance between them in graph 1198611015840 is bounded by 3119899+2

Based on the above conclusion we further analyze thebroadcast latency of SALB Assume Figure 1 describing anetworkwith sleeping schedule and let119901

119866(1199060 119906119899) be the path

between 119906 and V(1199060= 119906 and 119906

119899= V) with minimum latency

We also assume SL119886(1199060) lt SL

119886(1199061) lt SL

119886(1199062) lt lt

SL119886(119906119899) When V

0receives the broadcast message at SL

119886(1199060)

if each node in 119901119866(1199060 119906119899) retransmits the broadcast message

to its following neighbor along the path as long as receivingit node 119906

119899is able to receive the broadcast message with

the minimum latency SL119886(119906119899) minus SL

119886(1199060) If the broadcast

message is forwarded using the mechanism in SALB alongthe path 119901

1198611015840(1199060 119906119899)within the broadcast backbone 119861 at most

3119899+ 1 inversions will be encountered for example SL119886(1198890) ge

SL119886(1198860) ge SL

119886(1198861) ge SL

119886(1198891) ge ge SL

119886(119889119899) ge SL

119886(119906119899)

It is worth noting that SL119886(1199060) lt SL

119886(1198890) holds otherwise

SL119886(1199060) ge SL

119886(119906119899) which contradicts the assumption In

this case the transmission latency is SL119886(119906119899) minus SL

119886(1199060) +

(3119899 + 1)|119879| Let 1198711198751198611015840 (1199060 119906119899)

be the transmission latency alongpath 119901

1198611015840(1199060 119906119899) using the forwarding mechanism of SALB

and let 119871119901119866(1199060119906119899)be the minimum transmission latency along

path 119901119866(1199060 119906119899) 119871119901119866(1199060119906119899)has the minimum value of 119899 when

SL119886(119906119894+1

) = SL119886(119906119894) + 1 Hence we have

1198711198751198611015840 (1199060 119906119899)

119871119901119866(1199060119906119899)

leSL119886(119906119899) minus SL

119886(1199060) + (3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

= 1 +(3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

le 1 +(3119899 + 1) |119879|

119899le 1 + 4 |119879|

(3)

The equation holds when 119899 = 1The minimum broadcast latency 119871min in the network is

actually the maximum-minimum transmission latency fromthe broadcast source 119904 to each node in the network alongthe paths in graph 119866 Assume that the path in 119866 with thelatency 119871min is 119901119866(119904 119906

1015840) While using SALB according to (3)

the transmission latency of forwarding the broadcastmessagealong the path 119901

1198611015840(119904 1199061015840) in graph 119861

1015840 is less or equal to (4|119879| +

1)119871min This theorem holdsThe construction of virtual broadcast backbone domi-

nates the time and message complexities of SALB algorithmAccording to [7 25] the time andmessage complexities of theCDS constructing algorithm we used in forming the virtualbackbone of SALB are both 119874(119899) Therefore the time andmessage complexities of SALB are both 119874(119899) where 119899 is thesize of the WSN

52 Simulation Results We conduct simulations to evaluatethe performance of SALB on a costumed simulator developedusing PARSEC [29] which is a C-based distributed discrete-event simulation language In simulations the network israndomly deployed in a 200m lowast 200m dimension area Tomaintain reasonable network connectivity the radio radius ofeach node is set to 35m resulting in at least 05 nodes100m2and a node degree of at least 19 in the following experimentsEach node randomly chooses an active time-slot from 119879 Allresults are average of ten runs In each run the broadcastsource node is chosen randomly

We first observe the broadcast transmission of SALBIn this simulation we compared SALB with the modifiedclassical tree-based broadcast scheme [30] namely the Tree-algorithm The Tree-algorithm can be stated as followsgenerate a spanning tree of the network119866 rooted in the sourcenode 119904 and the broadcast finishes when each node on thistree sends message to all its children according to their activetime-slots Obviously total transmission of Tree-algorithm isexactly 119899 minus 1 We let |119879| = 20 to observe the impact ofnetwork size on the broadcast transmission As the networksize is scaling up the transmission of both Tree-algorithmand SALB increases (Figure 2) When the network size isrelatively small (eg 119899 lt 300) the transmission of SALB is abitmore than that of Tree-algorithmThat is becausewhen |119879|is fixed and the network size is small each node will choosea different active time-slot with a high probability In this


1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB

Figure 2 Impact of network size on transmission

540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)

Figure 3 Impact of |T| on transmission

case each dominator had to transmit to its dominatees oneby one which is similar to the unicast scenario On the otherhand there exist redundant paths between two dominatorsin the virtual backbone of SALB which also causes the resultHowever when the network size is large enough for example119899 gt 300 more nodes will have identical active time-slots andthus the active time-slot-oriented forwarding mechanism ofSALB can save mode transmission When 119899 gt 900 thetransmission of SALB is only 50 of the Tree-algorithmThen we fix the network size to 500 nodes to observe theimpact of |119879| on the transmission For the Tree-algorithmthe transmission remains unchanged since it is determinedby the network size For SALB the transmission increasesas |119879| becomes larger (Figure 3) When |119879| is small nodesshare identical active time-slots with a high probability andthus SALB can save more transmission (eg |119879| lt 60 in

800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)

Figure 4 Impact of network size on latency

45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT

Figure 5 Impact of network size on ratio to OPT

Figure 3) As |119879| increases nodes have different active time-slots gradually together with the redundant paths amongdominators leading to a bit more transmission than the Tree-algorithm

We then evaluate the broadcast latency of SALBWithoutconsidering the collision of wireless channel if each noderetransmits the broadcast message as long as receiving it thebroadcast will finish within the minimum latency namelyOPTWe compare the broadcast latency of SALBwithOPT inthe following simulations Firstwe fix |119879| = 100 to observe theimpact of network size on latency As the network is scalingup both the latency of SALB and OPT decrease (Figure 4)The reason behind is when |119879| is fixed the increase of nodewill make more of them share identical active time-slots Asa result in SALB one transmission of a dominator at sometime-slot can cover mode neighbor nodes accelerating thebroadcast process We also find that the broadcast latency ofSALB never exceeds 35 times of the OPT (Figure 5) Then


1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

Figure 6 Impact of |T| on latency

we fix network size to 500 nodes to see the impact of |119879|In accordance with theoretical analysis both the latency ofSALB and OPT increase linearly (Figure 6) That is becausein the cases with fixed network size and increasing |119879| fewof nodes share identical active time-slots Broadcast processhad to borrow the unicast method leading to the increase oflatency We also find that as |119879| is increasing the latency ofSALB remains within 3 times of OPT (Figure 7)

6 Discussion

In the design of SALB algorithm we apply a heuristic strategyto decrease the number of transmissions and the broadcastlatency However the two objectives always conflict witheach other Next we will illustrate an example We considera network shown as in Figures 8 and 9The period of sleepingschedule 119879 = 1 2 3 4 5 Node 119886 is the source node ofbroadcasting The number in the circle of a node meansthe active time-slot of the node and the underlined numbermeans the time of package arrives Tominimize the broadcastlatency the broadcasting schedule will be 119886 rarr 119888 119886 rarr

119887 119888 rarr 119891 and 119887 rarr 119889 119890 (Figure 8) The latency is 8 time-slots and the numbers of transmissions are 4 To minimizethe numbers of transmissions the broadcasting schedule willbe 119886 rarr 119887 119887 rarr 119888 119889 119890 and 119888 rarr 119891 (Figure 9) Thenumbers of transmissions are 3 and the broadcast latencyis the time of node 119891 receiving the data package 11 time-slots We can observe from this example that minimizing thebroadcast latency may cause the number of transmission tobe increasing and vice versa Therefore in the real scenariosa tradeoff between two objectives is required

7 Conclusion

In this paper we studied the broadcasting problem whileconsidering sleeping schedule in WSN First we formulatedthe sleeping schedule-aware broadcast algorithm Then we

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT

Figure 7 Impact of |T| on latency ratio to OPT

a

bc

d e

f35

3 3

1

8

63

0

8

5

Figure 8 Relationship of latency and transmission (a)

a

bc

d e

f35

3 3

1

8

8

0

8

5 11

Figure 9 Relationship of latency and transmission (b)

proposed a local broadcast algorithm SALB In SALB wemodified a classical local algorithm for constructing con-nected dominating set to form the broadcast backbone anddesigned a forwarding mechanism to handle the periodicallysleeping issue of nodes We proved that the number oftransmission of SALB is within 4(min(Δ |119879|) + 119888) (c isconstant) times of the optimal value and the latency is within4|119879| + 1 times of the optimal value Moreover simulationsresults showed that the performance of SALB is better thanthe tree-based broadcast algorithm In the best case the SLABsaved 50 transmission of the Tree algorithmAs the networkis scaling up and the period of sleeping schedule is increasingthe latency of SALB remains within the constant times of theoptimal value

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Acknowledgments

Thiswork is partly supported by theNational Natural ScienceFoundation of China (Grant nos 61202417 61073028 and61021062) the General Program of Science and Technol-ogy Development Project of Beijing Municipal EducationCommission (Grant no KM201411232013) and the Project ofShandongProvinceHigher Educational Science andTechnol-ogy Program under Grant no J13LN13

References

[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash105 2002

[2] S Y Ni Y C Tseng Y S Chen and J P Sheu ldquoThe broadcaststorm problem in a mobile Ad Hoc networkrdquo in Proceedings ofthe 5th Annual ACMIEEE International Conference on MobileComputing and Networking (MobiCom rsquo99) pp 151ndash162 1999

[3] W Lou and J Wu ldquoA cluster-based backbone infrastructurefor broadcasting in manetsrdquo in Proceedings of the InternationalParallel and Distributed Processing Symposium (IPDPS rsquo03) pp1530ndash2075 April 2003

[4] J Wu and L Wei ldquoForward-node-set-based broadcast in clus-tered mobile Ad Hoc networksrdquo Wireless Communications andMobile Computing vol 3 no 2 pp 155ndash173 2003

[5] W Lou and J Wu ldquoOn reducing broadcast redundancy in AdHoc wireless networksrdquo IEEE Transactions on Mobile Comput-ing vol 1 no 2 pp 111ndash122 2002

[6] I Stojmenovic M Seddigh and J Zunic ldquoDominating sets andneighbor elimination-based broadcasting algorithms in wire-less networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 13 no 1 pp 14ndash25 2002

[7] O Liang Y Ahmet Sekercioglu andNMani ldquoA low-cost flood-ing algorithm for wireless sensor networksrdquo in Proceedings ofthe IEEE Wireless Communications and Networking Conference(WCNC rsquo07) pp 3498ndash3503 March 2007

[8] I Chlamtac and S Kutten ldquoTree-based broadcasting in multi-hop radio networksrdquo IEEE Transactions on Computers vol 36no 10 pp 1209ndash1223 1987

[9] S C-H Huang P-J Wan X Jia H Du and W ShangldquoMinimum-latency broadcast scheduling in wireless Ad Hocnetworksrdquo in Proceedings of the 26th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo07) pp 733ndash739 May 2007

[10] R Mahjourian M Thai F Chen H Zhai R Tiwari and YFang ldquoAn approximation algorithm for conflict-aware broad-cast scheduling in wireless Ad Hoc networksrdquo in Proceedingsof the 9th ACM International Symposium on Mobile Ad HocNetworking and Computing (MobiHoc rsquo08) pp 331ndash340 May2008

[11] O Dousse P Mannersalo and P Thiran ldquoLatency of wirelesssensor networks with uncoordinated power saving mecha-nismsrdquo in Proceedings of the 5th ACM International Symposiumon Mobile Ad Hoc Networking and Computing (MoBiHoc rsquo04)pp 109ndash120 May 2004

[12] G Lu N Sadagopan B Krishnamachari and A Goel ldquoDelayefficient sleep scheduling in wireless sensor networksrdquo inProceedings of the 24th Annual Joint Conference of the IEEEComputer and Communications Societies (INFOCOM rsquo05) vol4 pp 2470ndash2481 March 2005

[13] QCao T Abdelzaher THe and J Stankovic ldquoTowards optimalsleep scheduling in sensor networks for rare-event detectionrdquo inProceedings of the 4th International Symposium on InformationProcessing in Sensor Networks (IPSN rsquo05) pp 20ndash27 April 2005

[14] A Keshavarzian H Lee L Venkatraman K ChitalapudiD Lal and B Srinivasan ldquoWakeup scheduling in wirelesssensor networksrdquo in Proceedings of the 7th ACM InternationalSymposium on Mobile Ad Hoc Networking and Computing(MOBIHOC rsquo06) pp 322ndash333 May 2006

[15] Y Gu and T He ldquoData forwarding in extremely low duty-cycle sensor networks with unreliable communication linksrdquoin Proceedings of the 5th ACM International Conference onEmbedded Networked Sensor Systems (SenSys rsquo07) pp 321ndash334November 2007

[16] P Kyasanur R R Choudhury and I Gupta ldquoSmart gossipan adaptive gossip-based broadcasting service for sensor net-worksrdquo in Proceedings of the IEEE International Conference onMobile Ad Hoc and Sensor Sysetems (MASS rsquo06) pp 91ndash100October 2006

[17] F Wang and J Liu ldquoDuty-cycle-aware broadcast in wirelesssensor networksrdquo in Proceedings of the 28th IEEE Conferenceon Computer Communications (INFOCOM rsquo09) pp 468ndash476April 2009

[18] J Hong J Cao W Li S Lu and D Chen ldquoMinimum-transmission broadcast in uncoordinated duty-cycled wirelessAd Hoc networksrdquo IEEE Transactions on Vehicular Technologyvol 59 no 1 pp 307ndash318 2010

[19] B Tang B Ye J Hong K You and S Lu ldquoDistributedlow redundancy broadcast for uncoordinated duty-cycledWANETsrdquo in Proceedings of the 54th Annual IEEE GlobalTelecommunications Conference (GLOBECOM rsquo11) December2011

[20] J Hong J Cao W Li S Lu and D Chen ldquoSleeping schedule-aware minimum latency broadcast in wireless Ad Hoc net-worksrdquo in Proceedings of the IEEE International Conference onCommunications (ICC rsquo09) pp 1ndash5 June 2009

[21] X Jiao W Lou J Ma J Cao X Wang and X Zhou ldquoDuty-cycle-aware minimum latency broadcast scheduling in multi-hop wireless networksrdquo in Proceedings of the 30th IEEE Inter-national Conference on Distributed Computing Systems (ICDCSrsquo10) pp 754ndash763 June 2010

[22] W Ye J Heidemann and D Estrin ldquoAn energy-efficientMAC protocol for wireless sensor networksrdquo in Proceedingsof the 21st Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo02) pp 1567ndash1576 June2002

[23] M Maroti B Kusy G Simon and A Ledeczi ldquoThe floodingtime synchronization protocolrdquo in Proceedings of the 2nd Inter-national Conference on Embedded Networked Sensor Systems(SenSys rsquo04) pp 39ndash49 November 2004

[24] J Wu W Lou and F Dai ldquoExtended multipoint relays todetermine connected dominating sets in MANETsrdquo IEEETransactions on Computers vol 55 no 3 pp 334ndash347 2006

[25] K M Alzoubi P-J Wan and O Frieder ldquoMessage-optimalconnected dominating sets in mobile Ad Hoc networksrdquo inProceedings of the 3rd ACM International Symposium on MobileAd Hoc Networking and Computing (MOBIHOC rsquo02) pp 157ndash164 June 2002

[26] S Guha and S Khuller ldquoApproximation algorithms for con-nected dominating setsrdquo Algorithmica vol 20 no 4 pp 374ndash387 1998


[27] P-JWan KM Alzoubi and O Frieder ldquoDistributed construc-tion of connected dominating set in wireless AdHoc networksrdquoMobile Networks and Applications vol 9 no 2 pp 141ndash1492004

[28] Y Wang and X-Y Li ldquoGeometric spanners for wireless Ad Hocnetworksrdquo in Proceedings of the 22nd International Conferenceon Distributed Systems (ICDCS rsquo02) pp 171ndash178 July 2002

[29] R Bagrodia R Meyer M Takai et al ldquoParsec a parallelsimulation environment for complex systemsrdquo Computer vol31 no 10 pp 77ndash85 1998

[30] A Juttner and A Magi ldquoTree based broadcast in Ad HocnetworksrdquoMobile Networks and Applications vol 10 no 5 pp753ndash762 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



when it is active so not all neighbors of a senor node canreceive the broadcast message by one transmission This dif-ference renders the broadcast problem more difficult in suchsituations Existing broadcast algorithms did not consider thesleeping schedule issues and thus are not suitable

To solve the sleeping schedule-aware broadcast problemwe practically propose a local algorithm in this papernamely the sleeping schedule-aware local broadcast (SALB)algorithm In SALB we first use a typical local MCDSconstruction algorithm to form a virtual broadcast backboneWith this virtual backbone we design an active slot-basedforwarding mechanism for each node which guaranteesthe success of broadcast and can help reduce transmissionredundancy and latency The numbers of transmissions forSALB are within 4(min(Δ |119879|)+119888) (c is constant) times of theoptimal value And the broadcast latency of SALB is within4|119879| + 1 times of the minimum value (Δ is the maximumdegree in the network |119879| is the scheduling period length)

The rest of this paper is organized as follows We reviewthe related work in Section 2 and present the models andassumption in Section 3 SALB is proposed in Section 4 Weevaluate its performance in Section 5 and discuss the tradeoffbetween the number of transmissions and the broadcastlatency in Section 6 In Section 7 we conclude this paper

2 Related Work

Data-transmission issues in duty-cycled WANETs haverecently attractedmuch of researchersrsquo attentionDousse et al[11] established a bound on the transmission latency of sensornetworks with uncoordinated schedule Lu et al provedthe NP-hardness of minimizing end-to-end communicationdelay in low-duty-cycle sensor networks in [12] Cao etal proposed the pipeline forwarding pattern for sensornetworks with a sleeping schedule to decrease the delay [13]Keshavarzian et al analyzed the delay of several knownwake-up patterns and proposed a new multiparent schedulingpattern for sensor networks in [14] Gu and He proposeda dynamic data forwarding scheme for extremely low-duty-cycle sensor networks based on the expected latency andreliability model [15] However these works mainly focus onthe latency issue caused by the sleep schedule and none ofthem refer to the broadcast problem

Since broadcast plays an important role in WSNs a lotof research work has been done on this area The simplestapproach for broadcast is blind flooding where each node isobligated to forward a packet upon receiving it for the firsttime However it has been shown that blind flooding can leadto serious redundancy and collisions a situation known asbroadcast storm [2] Therefore great effort has been madeby improving the flooding approach to reduce broadcastredundancy and collisions as well as broadcast latency Forexample [2 16] proposed probabilistic forwarding methodsto avoid massive redundant transmissions Based on theconstruction of virtual broadcast backbone and broadcastingalong the backbone [3ndash7] proposed different technologiesto reduce broadcast redundancy Specifically much recentresearch has been done to minimize the broadcast transmis-sions and minimize the broadcast latency based on different

Table 1 Notations

119899 The number of nodes in the network119879 The period of sleeping scheduleΔ Themaximum degree of nodes in the network119873(V) The set of neighbors of node V119863(V) The set of 1-hop neighbor dominators of node V1198632(V) The set of 2-hop neighbor dominators of node V

SL119886(V) The active time-slot of node V

network models Generally both the minimum transmissionbroadcast problem and the minimum latency broadcastproblem are NP-hard and a lot of efficient algorithms havebeen proposed [3ndash10]

Recently some researches focusing on the sleepingschedule-aware broadcast problem have emerged Wang etal discussed the broadcast problem in duty-cycle sensornetworks in [17] Hong et al proposed a series of workon the minimum-redundancy broadcast problem for duty-cycle wireless ad hoc networks [18 19] The other topic ofminimum-latency broadcast problem has been investigatedin [20 21] However none of them proposes a local algo-rithm for sensor network considering both transmission andlatency issues of broadcast

3 Model and Assumption

We assume that 119899 sensors node are deployed in a two-dimensional plane with equal maximum transmitting rangeof one unitThenetwork can bemodeled as a connectedUDG119866(119881 119864) where 119881 is the set of nodes and 119864 is the edge set Anedge 119906 V isin 119864 if and only if the distance between nodes uand v is within each otherrsquos communication range Unlike theliterature focusing on tuning sleeping schedule [12ndash14] wefollow the assumption in [11] where each node determinesits sleeping schedule completely and uncoordinatedly Weassume that the scheduling period 119879 is divided into|119879|time-slots with fixed and equal length denoted by 1 2 |119879|

accordingly We also assume that each node v randomlychooses an active time-slot SL

119886(V) isin 119879 independently Each

time-slot is assumed to be long enough for sending orreceiving a data packet [12] The contention and collisionissues of wireless channel are assumed to process by theMACprotocols for example S-MAC [22] Therefore we will notneed to consider the impact of factors like channel conflictFollowing the models in [12 15] we assume that a node canwake up to transmit at any time but can receive only inits active time-slot The set of sending time-slots of node Vis SL119904(V) The global time synchronization is guaranteed by

protocols like flooding time synchronization protocol (FTSP)[23]

The notations used in this paper are listed in Table 1

31 Problem Formulation We consider the multisourcebroadcast in this paper in which each node in the network ispossible to broadcast the data packets to all the other nodesIn the general WSN with the benefit of broadcasting nature




119904(V) in





119904(V) COV119894(V)) = 119881



0 V1 V

119896 V119896+1


119896and V119896+1

if SL119886(V119896) le SL

119886(V119896+1




119886(119888) minus SL











120578 =

1003816100381610038161003816119906 | 119906 isin 119873 (V) SL119886(V) lt SL

119886(119906)

1003816100381610038161003816

|119873 (V)| (1)








Algorithm 1


Algorithm 2







2(119906) for the









2(119906)




2(119906) 119906 will






119886(V) + 1)119898119900119889 |119879|




Algorithm 3










2is










119872 = |119878| (min (Δ |119879|) + 1198972+ 21198973)

le (min (Δ |119879|) + 119888) (4MCDS + 1)

le (min (Δ |119879|) + 119888) (4119877min + 1)

(2)

The theorem holds




unu0 u1 u2

a0 a1 a2 a3











119906 = 1199060 V = 119906



119894


119889119894119906119894119906119894+1

119889119894+1


119894and

119889119894+1






119866(1199060 119906119899) be the path

between 119906 and V(1199060= 119906 and 119906



119886(1199061) lt SL

119886(1199062) lt lt

SL119886(119906119899) When V


119886(1199060)









SL119886(1198860) ge SL

119886(1198861) ge SL

119886(1198891) ge ge SL

119886(119889119899) ge SL

119886(119906119899)



SL119886(1199060) ge SL



119886(1199060) +

(3119899 + 1)|119879| Let 1198711198751198611015840 (1199060 119906119899)





SL119886(119906119894+1

) = SL119886(119906119894) + 1 Hence we have

1198711198751198611015840 (1199060 119906119899)

119871119901119866(1199060119906119899)

leSL119886(119906119899) minus SL

119886(1199060) + (3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

= 1 +(3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

le 1 +(3119899 + 1) |119879|

119899le 1 + 4 |119879|

(3)





1198611015840(119904 1199061015840) in graph 119861







1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB


540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)



800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)


45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT





1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119904(V) in





119904(V) COV119894(V)) = 119881



0 V1 V

119896 V119896+1


119896and V119896+1

if SL119886(V119896) le SL

119886(V119896+1




119886(119888) minus SL











120578 =

1003816100381610038161003816119906 | 119906 isin 119873 (V) SL119886(V) lt SL

119886(119906)

1003816100381610038161003816

|119873 (V)| (1)








Algorithm 1


Algorithm 2







2(119906) for the









2(119906)




2(119906) 119906 will






119886(V) + 1)119898119900119889 |119879|




Algorithm 3










2is










119872 = |119878| (min (Δ |119879|) + 1198972+ 21198973)

le (min (Δ |119879|) + 119888) (4MCDS + 1)

le (min (Δ |119879|) + 119888) (4119877min + 1)

(2)

The theorem holds




unu0 u1 u2

a0 a1 a2 a3











119906 = 1199060 V = 119906



119894


119889119894119906119894119906119894+1

119889119894+1


119894and

119889119894+1






119866(1199060 119906119899) be the path

between 119906 and V(1199060= 119906 and 119906



119886(1199061) lt SL

119886(1199062) lt lt

SL119886(119906119899) When V


119886(1199060)









SL119886(1198860) ge SL

119886(1198861) ge SL

119886(1198891) ge ge SL

119886(119889119899) ge SL

119886(119906119899)



SL119886(1199060) ge SL



119886(1199060) +

(3119899 + 1)|119879| Let 1198711198751198611015840 (1199060 119906119899)





SL119886(119906119894+1

) = SL119886(119906119894) + 1 Hence we have

1198711198751198611015840 (1199060 119906119899)

119871119901119866(1199060119906119899)

leSL119886(119906119899) minus SL

119886(1199060) + (3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

= 1 +(3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

le 1 +(3119899 + 1) |119879|

119899le 1 + 4 |119879|

(3)





1198611015840(119904 1199061015840) in graph 119861







1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB


540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)



800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)


45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT





1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Algorithm 1


Algorithm 2







2(119906) for the









2(119906)




2(119906) 119906 will






119886(V) + 1)119898119900119889 |119879|




Algorithm 3










2is










119872 = |119878| (min (Δ |119879|) + 1198972+ 21198973)

le (min (Δ |119879|) + 119888) (4MCDS + 1)

le (min (Δ |119879|) + 119888) (4119877min + 1)

(2)

The theorem holds




unu0 u1 u2

a0 a1 a2 a3











119906 = 1199060 V = 119906



119894


119889119894119906119894119906119894+1

119889119894+1


119894and

119889119894+1






119866(1199060 119906119899) be the path

between 119906 and V(1199060= 119906 and 119906



119886(1199061) lt SL

119886(1199062) lt lt

SL119886(119906119899) When V


119886(1199060)









SL119886(1198860) ge SL

119886(1198861) ge SL

119886(1198891) ge ge SL

119886(119889119899) ge SL

119886(119906119899)



SL119886(1199060) ge SL



119886(1199060) +

(3119899 + 1)|119879| Let 1198711198751198611015840 (1199060 119906119899)





SL119886(119906119894+1

) = SL119886(119906119894) + 1 Hence we have

1198711198751198611015840 (1199060 119906119899)

119871119901119866(1199060119906119899)

leSL119886(119906119899) minus SL

119886(1199060) + (3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

= 1 +(3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

le 1 +(3119899 + 1) |119879|

119899le 1 + 4 |119879|

(3)





1198611015840(119904 1199061015840) in graph 119861







1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB


540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)



800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)


45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT





1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119886(V) + 1)119898119900119889 |119879|




Algorithm 3










2is










119872 = |119878| (min (Δ |119879|) + 1198972+ 21198973)

le (min (Δ |119879|) + 119888) (4MCDS + 1)

le (min (Δ |119879|) + 119888) (4119877min + 1)

(2)

The theorem holds




unu0 u1 u2

a0 a1 a2 a3











119906 = 1199060 V = 119906



119894


119889119894119906119894119906119894+1

119889119894+1


119894and

119889119894+1






119866(1199060 119906119899) be the path

between 119906 and V(1199060= 119906 and 119906



119886(1199061) lt SL

119886(1199062) lt lt

SL119886(119906119899) When V


119886(1199060)









SL119886(1198860) ge SL

119886(1198861) ge SL

119886(1198891) ge ge SL

119886(119889119899) ge SL

119886(119906119899)



SL119886(1199060) ge SL



119886(1199060) +

(3119899 + 1)|119879| Let 1198711198751198611015840 (1199060 119906119899)





SL119886(119906119894+1

) = SL119886(119906119894) + 1 Hence we have

1198711198751198611015840 (1199060 119906119899)

119871119901119866(1199060119906119899)

leSL119886(119906119899) minus SL

119886(1199060) + (3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

= 1 +(3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

le 1 +(3119899 + 1) |119879|

119899le 1 + 4 |119879|

(3)





1198611015840(119904 1199061015840) in graph 119861







1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB


540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)



800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)


45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT





1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












unu0 u1 u2

a0 a1 a2 a3











119906 = 1199060 V = 119906



119894


119889119894119906119894119906119894+1

119889119894+1


119894and

119889119894+1






119866(1199060 119906119899) be the path

between 119906 and V(1199060= 119906 and 119906



119886(1199061) lt SL

119886(1199062) lt lt

SL119886(119906119899) When V


119886(1199060)









SL119886(1198860) ge SL

119886(1198861) ge SL

119886(1198891) ge ge SL

119886(119889119899) ge SL

119886(119906119899)



SL119886(1199060) ge SL



119886(1199060) +

(3119899 + 1)|119879| Let 1198711198751198611015840 (1199060 119906119899)





SL119886(119906119894+1

) = SL119886(119906119894) + 1 Hence we have

1198711198751198611015840 (1199060 119906119899)

119871119901119866(1199060119906119899)

leSL119886(119906119899) minus SL

119886(1199060) + (3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

= 1 +(3119899 + 1) |119879|

SL119886(119906119899) minus SL

119886(1199060)

le 1 +(3119899 + 1) |119879|

119899le 1 + 4 |119879|

(3)





1198611015840(119904 1199061015840) in graph 119861







1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB


540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)



800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)


45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT





1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1000

900

800

700

600

500

400

300

200

100

10009008007006005004003002001000

Tran

smiss

ion

Nodes (|T| = 20)

TreeSALB


540

520

500

480

460

440

420

400

380

360

20 40 60 80 100 120 140 160 180 200

Tran

smiss

ion

TreeSALB

|T| (n = 500)



800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

Late

ncy

(slo

t)

OPTSALB

1000900800700600500400300200100

Nodes (|T| = 100)


45

40

35

30

25

20

15

10

051000900800700600500400300200100

Nodes (|T| = 100)

Radio versus OPT





1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1100

1000

900

800

700

600

500

400

300

200

100

0

Late

ncy

(slo

t)

OPTSALB

20 40 60 80 100 120 140 160 180 200

|T| (n = 500)



6 Discussion



7 Conclusion


20 40 60 80 100 120 140 160 180 200

|T| (n = 500)

35343332313029282726252423222120

Radio versus OPT


a

bc

d e

f35

3 3

1

8

63

0

8

5


a

bc

d e

f35

3 3

1

8

8

0

8

5 11






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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