FernUniversität Hagen: Multimedia and Internetapplications 1

VoroDSPTA P2P-Network for

Spatial Objects

FernUniversität Hagen

InformatikzentrumD-58084 Hagen

D. Heutelbeck, C. Sergel, M. Hemmje

2008

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Idea: Use of Location- Knowlegde

• Information (Sensors, Maps, Databases, personal information)

• Bound to specific location (coordinate, line, shape)

• Applications: Navigation, Home Automation, Geographic information systems (GIS)...

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Presentation Goals

• To provide a location-based Search Algorithm in P2P systems with DSPT as spatial index

• To provide a topologically aware overlay construction in a P2P system based on Voronoi Diagram

• To present research activities????

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DSPTDistributed Space Partition Tree

How share spatial information in P2P system?

• an indexstructure support area of services - a subset of search-space

• Search key: simple (lo,o) tuple

• Distribution of key: – Unpredictable,

dynamic, variable

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RectNet DSPT Implementation

• Adaptiv Binary tree shaped network topology

• recursive space partitioning for load-balancing

• Problem: Clusterhead responsible for routing of all inter-subcluster communication scale not well

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Voronoi Diagram

• Is a decomposition of a metric space Rd

• Each node pV defines a region V(p) consituted of all points closer to p than or equally distant to any other node.

• V(p)={y Rd w V. d(y,u) d(y,w) }

• V(p) is interior of a convex polytope

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Fortune‘s Sweepline Algorithm

• Computes intersection of scaning plane with n points– Intersection of parabolic

arcs is a bisector of 2 neighboring points

– Point events– Circle events

• Complexity for computing VD in worst case with n = # nodes : – O(n log n) time, – O(n) storage

Source: Èuk Roman Construction of VD using Fortune‘s method (1999)

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Voronoi Overlay

• Routing advantage– Greedy routing– Short paths– Locality

• Data advantage– Storing and retrieval

of spatial objects– Spatial relationships:

Query intersection, -inclusion, exact match

Hipparchus Voronoi-based index Source:www.geodyssey.com

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Voronoi Overlay (2)

• 2 dimensional key space

• Peer‘s position is generator in VD

• Each peer has local Voronoi-region.

• Union of all Voronoi-region is global VD

• Node degree: O(1) at average

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Voronoi Overlay (3)

• Each peer computes local state of view of global VD• Neighborhood is defined by computing local VD• Local VD provides enough information about neighbor‘s

Voronoi regions for optimal decisions of forwarding messages

Global view of VD local view of VD

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Greedy Routing

• Finding paths between nodes without complete knowledge of graph structure

• Deciding for local processing of received message and/or forwarding it to neighbors

• Guaranteed delivering but not always most optimal

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VoroDSPT

Every peer • generates own

Voronoi Diagram (VD)

• manages network connectivity

• stores, updates and deletes locations l_o

• executes spatial queriesArchitecture of VoroDSPT

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Joining

1. Joiner sends WantoJoin message to bootpeer

2. Forwarding to nearest peer

3. a Peer-message is send to Joiner, who computes local VD and

4. who sends Hello-m. to new neighbors

5. A JoinAck is send to nearest peer

6. Neighbors checks local VD and answer with NewNeighbor or Neighborleave message

Joining of VoroDSPT-Peer

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Leaving / Failure

• With Disconnect message controlled leaving

• Sending Alive messages to all neighbors detection of failure, if no response of Alive-message

• after a time limit updating of local VD, informing neighbors The alive-process

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DSPT Service

• Publishing spatial objects in a p2p system– put (o,l_o)– remove(o,l_o)

• Querying for spatial locations– inclusionQuery(q)– intersectionQuery(

q)– equalQuery(q)

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DSPT-Storage

1. A spatial object (o,l_o) is stored in LocalStore of peer p.

2. A storage-process is started for publishing location l_o.

3. Location l_o is checked of intersection of local VD-cell

4. If positive, l_o is stored in RemoteStore of p, otherwise message, containing l_o, is created and greedy routed

5. All peers, whose VD-cell intersects location, store it in their RemoteStore and start a process for responsing data updates.

Global and local view of VD

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DSPT-Search

1. A query qLocation is stored in Querystore of peer x.

2. A query-process is started for query q

3. Message, containing q, is greedy routed

4. Query-location is checked of intersection/inclusion or equality of stored objects

5. Positiv answers send back directly to x.

6. Peer x contacts peer p directly for getting real object.

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Redundance

• Storage of spatial objects causes redundant messages, e.g. – first storage of

location(blue arrows)

– Updating location– Answers of a query

(green arrows)

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Lands End

• Lands End marks a point with the smallest x- value of location

• Served to reduce redundant messages for updating objects

• Release source peer

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Long Distance Links (LDL)

• In case of a large number of nodes network-diameter increases causes serious communication delay

• Solution: LDL– reduce routing load– reduce latency– increase performance

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Long Distance Links (2)

• p gets node-adress informations and shape of Voronoi-cells from LandEnds-peers

• LDLs are organized from source peer p

• LDL supports search for queried locations

the more storage the more LDLs are created

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Scalability

• mean Node degree =6

• mean pathlength of O (log N)

• Max pathlength of O(N)

• small network diameter with LDL

• simple greedy routing algorithm

• efficient structured overlay with VD

• dynamic join and leave of nodes

• Dynamic distributed storage of spatial location-objects

• distribution of traffic with use of LandsEnd and LDLs

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Load Balancing

Goals:• Prevent bottleneck• Even distributed data

among participantsProblems:• Data locality prevents

even distribution• Multiple storage of

locations on same key-space

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Path Length

• Simulated global Voronoi-overlay

• Experiments with 20 up to 5000 generated nodes

• Each node contacts all the others

• Count path length in hops for each experiment

Mean path lengths

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Path Length (2)

• Path length = #hops per path

• In VD a path is a direct acyclic shortest graph

• Path between 2 arbitrary nodes have to be measured separately

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Path Length (3)

• 20 nodes randomly generated in a 2-D VD– Mean path length is 2

hops– Max path lengths is 7

• 20 collinear generated nodes– Mean path length is 7

hops– worst path length is 20