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Target-Oriented Scheduling in Directional Sensor Networks

Yanli Cai, Wei Lou, Minglu Li ,and Xiang-Yang Li*

The Hong Kong Polytechnic University, Hong Kong*Illinois Institute of Technology

INFOCOM 2007

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Outlines

Introductions Multiple Directional Cover Sets Problem (MD

CS) Solutions to the MDCS problem

Progressive algorithm Prog-Resd algorithm Feedback algorithm

Simulation Results Conclusions

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Introductions

omni-directional sensor Have an omni-angle of sensing range.

[10] M. Cardei, M. T. Thai, Y. Li, and W. Wu, “Energy-efficient target coverage in wireless sensor networks,” in IEEE INFOCOM, 2005.

directional sensor Video sensors, ultrasonic sensors, and infrared sensors. The sensing region of each direction of a directional sensor is a s

ector of the sensing disk centered at the sensor with a sensing radius.

Each sensor has a uniform sensing region and the sensing regions of different directions of a sensor do not overlap.

The objective of this paper To maximize the network lifetime of a directional sensor network

network lifetime : the time duration when each target is covered by the work direction of at least one active sensor.

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Introductions

cover set A subset of directions of the sensors, in which the directions

cover all the targets. No more than one direction of a sensor can be in a cover set.

directional cover set problem (DCS) “Finding a cover set” and it is NP-complete.

non-disjoint cover sets Organize the directions of sensors into non-disjoint subsets, each

of which is a cover set, and allocate the work time for each cover set.

Allow a direction or a sensor to participate in multiple cover sets. multiple directional cover sets problem (MDCS)

Finding non-disjoint cover sets and allocating the work time for each of them to maximize the network lifetime.

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Multiple Directional Cover Sets Problem (MDCS) Notations

M : the number of targets. N : the number of sensors. W : the number of directions per sensor. am : the mth target, 1 m M. si : the ith sensor, 1 i N. di,j : the jth direction of the ith sensor, 1 i N, 1 j W.

di,j = { am | am is covered by di,j , am A } and si = {di,j | j = 1…W} . A : the set of targets. A = {a1, a2, …, aM} S : the set of sensors. S = {s1, s2, …, sN} D : the set of the directions of all the sensors.

D = {di,j | i = 1…N, j = 1…W} Dk = {di,j | ti,j,k > 0, di,j D} : the kth cover set of work directions. tk : the work time of the kth cover set of directions, ti,j,k : the work time of the direction di,j in the kth cover set of directions Li: the lifetime of a sensor si

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Each sensor has an initial lifetime of 1 (time unit). Fig. 1(a), D1 ={d1,3, d3,1} with 0.5, D2 ={d1,3, d2,2} with 0.5, and D3 = {d2,2,

d3,1} with 0.5. This results in a network lifetime of 1.5. Fig. 1(b), D1 = {d1,3, d2,2} with its available work time 1. This results in a

network lifetime of 1.

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Multiple Directional Cover Sets Problem (MDCS) Model the MDCS as a Mixed Integer Programming

(MIP) problem. A directional sensor network with

a set A of M targets a set S of N sensors a set D of directions Each sensor si S has W directions and an initial lifetime of Li

Organize the directions in D into K cover sets. The kth cover set is denoted as Dk, with the work time tk.

A direction di,j is allowed to participate into multiple cover sets.

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Multiple Directional Cover Sets Problem (MDCS)

a boolean variable :

The objective :

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Multiple Directional Cover Sets Problem (MDCS) Let ti,j,k = xi,j,k * tk

ti,j,k : the work time of di,j in the cover set Dk Get the following Linear Mixed Integer Programming (LMIP) problem.

The objective :

relax

0 ti,j,k t

k

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Progressive Algorithm

Compute several cover sets and their corresponding work time which is accumulated to the total network lifetime in each iteration. Step 1 : solve the LP problem and get the optimal solution of tk and ti,j,k

conflicting directions More than one direction of a sensor is in Dk and these directions conflict with each ot

her. non-conflicting direction

Only one direction of the sensor is in Dk

conflicting direction elimination process The process of removing the conflicting directions in Dk to make it a cover set.

Step 2 :If the update cover set Dk ≠ 0, then call the direction selection process.

Step 3 : update the residual lifetime of any selected sensor si using the work time t*k of the cover set D*k

Repeat Step 1 ~ Step 3 until the lifetime computed in the current iteration is less than a small positive value of .

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D = {d1,1, d1,2, d1,3, …, d5,1, d5,2, d5,3}. Assume Dk = {d1,3, d2,1, d2,3, d3,1, d3,3, d4,1, d4,3, d5,1} and the work time of the corresponding directions in Dk is {0.8, 0.2, 0.8, 0.2, 0.8, 0.2, 0.8, 0.2}.Two non-conflicting directions d1,3 with longer work time 0.8 and d5,1 with work time 0.2, so d1,3 is selected. Get U = {a1} and then remove a1 from A’ . Get V = {d1,3, d2,1}, where d1,3 is a non-conflicting direction and d2,1 conflicts with d

2,3. Add d1,3 to Dk and remove both d1,3 and d2,1 from D’k. Finally, we get Dk = {d1,3, d2,3, d3,3, d4,3} with {0.8, 1.0, 1.0, 1.0}.

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Dk = {d1,1, d1,3, d2,1, d2,3, d3,1, d3,3, d4,1, d4,3, d5,1, d5,3, d6,1, d6,3} and the work time of each direction in Dk is {0.2, 0.8, 0.2, 0.8, 0.2, 0.8, 0.2, 0.8, 0.2, 0.8, 0.2, 0.8}. There is no non-conflicting direction in D’k, and we select d1,3 with its work time 0.8, d1,1 conflicts with d1,3, so d1,1 is removed from D’k. The direction d1,3 is a non-conflicting direction in D’k after d1,1 is removed. Finally, we get Dk = {d1,3, d2,3, d3,3, d4,3, d5,3, d6,3} with { 1.0, 1,0, 1.0, 1.0, 1.0, 1.0}.

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Direction Selection Process

To save energy, only a subset of Dk can be selected. Select the direction di,j Dk that satisfies ti,j,k > t*k and

has the longest work time, to cover some uncovered targets each time.

Repeat selecting another direction from Dk to D*k until all the targets are covered by the selected directions.

Then, remove redundant directions in D*k Because the targets covered by some directions formerly s

elected into D*k may be totally covered by the ones selected into D*k later, which causes redundancy.

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Prog-Resd Algorithm

Direction selection process of Progressive algorithm The direction with the longest work time is selected each ti

me. Prog-Resd algorithm takes into consideration the re

sidual lifetime of sensors. This algorithm differentiates from the Progressive al

gorithm only in the direction selection process. Select a cover set that has the longest residual lifeti

me Li to cover some uncovered targets each time.

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Feedback Algorithm

Too many cover sets may be inefficient or impractical. Frequently switching sensors from one direction to another may not be

easy for physical reasons. Too many cover sets mean too many state transition periods

Lead to the occurrence of some targets may not be covered during the state transition period.

Feedback that utilizes the results obtained from the previous iterations and finds a group of cover sets in the last iteration. Then use the results obtained in previous iterations as a feedback to the next iteration. This algorithm is more useful and practical because it generates no more

than K cover sets totally. (fewer cover sets) The LP problem, the conflicting direction elimination process, and the

direction selection process are also used. In each iteration of the Feedback algorithm, we only determine one cover

set from the solution to the LP problem, and add the constraints to the LP problem in the next iteration. Then we solve the updated LP problem again to get the next cover set.

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Simulation Results

Simulations running on a computer with 3 GHz CPU and 1 GB memory.

The optimization toolbox in Matlab is used to solve the LP problem.

N sensors with sensing radius r and M targets are deployed uniformly in a region of 400m 400m.

Each sensor has W directions. Each algorithm runs 10 times through random place

ment of sensors and targets. The Progressive algorithm and the Prog-Resd algorithm, se

t = 0.001. The Feedback algorithm, set δ= 0.0001.

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The network lifetime increases almost linearly when the number of sensors increases. The Feedback algorithm has te best performance.

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The network lifetime increases almost linearly when the sensing radius increases.

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The network lifetime drops quickly when M varies from 1 to 2, and then drops relatively slowly when M varies from5 up to 20.

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The network lifetime is almost linear to W.

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The runtime of the Feedback algorithm is longer than the other two algorithms.

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•Both the Progressive algorithm and the Prog-Resd algorithm generate much more cover sets than the Feedback algorithm.•Fewer cover sets with longer work time aremore efficient and practical.

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Conclusions

Study the problem of the multiple directional cover sets (MDCS).

Present the Progressive, Prog-Resd, and Feedback algorithm to solve the multiple directional cover sets (MDCS) problem.

Future work Design distributed algorithms to prolong the netwo

rk lifetime of a directional sensor network.

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References

[10] M. Cardei, M. T. Thai, Y. Li, and W. Wu, “Energy-efficient target coverage in wireless sensor networks,” in IEEE INFOCOM, 2005.

[11] H. Liu, P. Wan, C. Yi, X. Jia, S. Makki, and P. Niki, “Maximal lifetime scheduling in sensor surveillance networks,” in IEEE INFOCOM, 2005.

[12] M. X. Cheng, L. Ruan, and W. Wu, “Achieving minimum coverage breach under bandwidth constraints in wireless sensor networks,” in IEEE INFOCOM, 2005.

[13] H. Ma and Y. Liu, “On coverage problems of directional sensor networks,” in MSN, 2005.

[14] J. Ai and A. A. Abouzeid, “Coverage by directional sensors in randomly deployed wireless sensor networks,” Journal of Combinatorial Optimization, vol. 11, no. 1, pp. 21–41, Feb. 2006.

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Target Coverage Problem (1/5) Definition： Target Coverage Problem(TCP)

m targets with known location n sensors randomly deployed in the closed proximity of the targets schedule the sensor nodes activity all the targets are continuously observed and network lifetime is ma

ximized.

Scheduling mechanismStep1、 Sensors send their location information to the BS

Step2、 BS executes the sensor scheduling algorithm and broadcasts the schedule when each node is activ

e

Step3、 Every sensor schedules itself for active/sleep intervals

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Maximum Set Covers (2/5)

Definition：MSC Problem C: set of sensors （ n sensors ）

every sensor can be part of more than one set assume each sensor’s lifetime is 1

R: set of targets （ m targets ） Find a family of set covers S1, …, Sp with time wei

ght t1,…, tp in [0,1]

Goal： to maximize t1+…+ tp

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Disjoint set (3/5)

S1 = {s1, s2} t1=1

S2 = {s3, s4} t2=1 Lifetime G = 2

R = {r1, r2, r3}

C = {s1, s2, s3, s4}

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Maximum Set Covers (4/5)

S1 = {s1, s2} t1 = 0.5S2 = {s2, s3} t2 = 0.5S3 = {s1, s3} t3 = 0.5S4 = {s4} t4 = 1

Lifetime G = 2.5

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Solutions To Compute Maximum Set Covers (5/5) LP-MSC Heuristic Greedy-MSC Heuristic