An Efficient Pre-Computation Technique for Approximation KNN Search in Road Networks

1. An Efficient Pre-Computation Technique for ApproximationKNN Search in Road Networks Guang-Zhong Sun, Zhong Zhang, Jing Yuan National high performance centre at Hefei University of Science and Technology of China This work was supported by the National Science Foundation of China and Microsoft Research Asia Internet Service Theme Research Program

2. Motivation • Hefei city is a small city, becoming larger • The area of Hefei city doubled since 2005 • Lots of roads were constructed/re-constructed • Traffic Management Center at Hefei decided to build one management system Before reconstructed, Sep 2006 After reconstructed, Sep 2008

3. KNN Problem • There are m moving objects in road network, given a point at road, to find K-Nearest Neighbor (KNN) set from the m objects • Real-time requirement is critical • Objects are moving • Objects can appear/disappear at any time • On-line computation distance value using Dijkstra algorithm does not work

4. Basic Idea • General idea: using pre-computation • Compute and store all distance value between all pairs in the road network • Perform some simple operation to answer the queries in the on-line processing • Difficulty: space complexity is high, O(n2) • 210GB, when the # of node is about 1.7 × 105 • Using high performance computer • Main goal：reduce the requirement of memory • Systems can be running in a common PC

5. Main Idea • Input data are not exact • Weight value in the road network is the length of the road, which is just an approximation. • Other important factors: traffic light, traffic jam, etc. • Positions of moving objects are also not exact. • GPS devices are not 100% accurate: orbital error, receiver noise, etc • Assumption: approximation is accepted. • By that, to reduce required memory size

6. New Problem • Approximation KNN • δis error bound of approximation • Road network is same as KNN problem • There are m moving objects in road network, given a query point q, to find a set S from the m objects, for any o in S and any w not in S d(o, q) ≤ d(w, q) + δ

7. Distance Approx. • Choose an appropriate representative nodes set R For each node v in V, it has one and only one representative node r(v) in R • Only compute the distance between any pairs in R(space is O(|R|2)) • The distance between any two nodes is approximated as the distance between their representative nodes Approximation of distance is bounded by To find R, with small size, so that the longest distance of a node from the nearest node in R is small enough.

8. To find Representative Nodes Set • Two NP-hard problem • Given error bound δ, minimize size of set R • Given size of set R, minimize error boundδ • An simple heuristic algorithm to choose the representative nodes set, when error bound δis given.

9. Experimental evaluation • Data set: San Francisco road networks • 221,801 road segments and 174,955 nodes • Common PC • Intel Mobile Core2 Duo SP9400 CPU(2.4GHz) and 4G main memory

10. Experimental evaluation

11. Conclusion • Trade-off between approximation and cost • Size of required memory is significantly reduced • Approximation of distance value between any pairs was well bounded • Core work is on distance retrieval in networks • KNN is just an application • Future work • More sophisticated heuristics algorithms to find representative nodes set • Real application

12. Thanks!