1. FernUniversität Hagen:Multimedia and Internetapplications1 VoroDSPT A P2P-Network for Spatial Objects FernUniversität Hagen Informatikzentrum D-58084 Hagen D. Heutelbeck, C. Sergel, M. Hemmje 2008

2. 2 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)...

3. 3 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????

4. 4 DSPT Distributed Space Partition Tree How share spatial information in P2P system? an indexstructure support area of services - a subset of search-space Search key: simple (l o,o) tuple Distribution of key: –Unpredictable, dynamic, variable

5. 5 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

6. 6 Voronoi Diagram Is a decomposition of a metric space R d Each node p  V defines a region V(p) consituted of all points closer to p than or equally distant to any other node. V(p)={y  R d   w  V. d(y,u)  d(y,w) } V(p) is interior of a convex polytope

7. 7 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)

8. 8 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

9. 9 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

10. 10 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

11. 11 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

12. 12 VoroDSPT Every peer generates own Voronoi Diagram (VD) manages network connectivity stores, updates and deletes locations l_o executes spatial queries Architecture of VoroDSPT

13. 13 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

14. 14 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

15. 15 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)

16. 16 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

17. 17 DSPT-Search 1.A query q  Location 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.

18. 18 Redundance Storage of spatial objects causes redundant messages, e.g. –first storage of location (blue arrows) –Updating location –Answers of a query (green arrows)

19. 19 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

20. 20 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

21. 21 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

22. 22 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

23. 23 Load Balancing Goals: Prevent bottleneck Even distributed data among participants Problems: Data locality prevents even distribution Multiple storage of locations on same key- space

24. 24 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

25. 25 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

26. 26 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