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Processing proximity relations in road networks. Zhengdao Xu , Hans-Arno Jacobsen. SIGMOD Conference 2010: 243-254

Processing proximity relations in road networks. Zhengdao Xu , Hans-Arno Jacobsen. SIGMOD Conference 2010: 243-254. Presented by – Aditi Srivastava. Introduction. Motivation : Goal of the paper :

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Processing proximity relations in road networks. Zhengdao Xu , Hans-Arno Jacobsen. SIGMOD Conference 2010: 243-254

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  1. Processing proximity relations in road networks. ZhengdaoXu, Hans-Arno Jacobsen.SIGMOD Conference 2010: 243-254 Presented by – AditiSrivastava

  2. Introduction Motivation : Goal of the paper : Develop spatio-temporal query processing techniques for such scenarios in road networks.

  3. Contribution of the paper- • 3 types of location constraints defined to represent proximity relations in road networks • Efficient query processing algos to compute these • Novel graph partitioning to index the moving objects • An extension of the approach to evaluate constraints over past movement histories and projected movement trajectories

  4. Definitions Given a set P of moving objects on the road network graph,

  5. Each of the above proximity relations induces a location constraint as follows, where d is referred to as the alerting distance: • The pairwise constraint is of the form mpd(P) < d. It is satisfied if the max-pairwise-distance of P is less than d. 2. The min-sum constraint is of the form msd(P) < d. It is satisfied if the min-sum-distance of P is less than d. 3. The min-max constraint is of the form mmd(P) < d. It is satisfied if the min-max-distance of P is less than d.

  6. Computing Proximity relations Max pairwise distance Min sum distance – edge split is candidate for MSC (Minimum Sum Center) By triangle inequality

  7. Min Sum Distance Let the position of x on the edge be θ (or be distance θ[va, vb]away from va), then the shortest path from pi to x is a piecewise linear function, Dpi (θ), of θ, with split point θespi : The sum-distance from object set P to x is a piecewise linear function: sd(x) = ∑PpiEPDpi (θ) and the min-sum-distance on the edge is min0≤θ≤1 sd(x).

  8. Prune the e-splits search space using Lemma 1 And calculate MSC (min-sum-center)

  9. Min-max-distance (Refer fig : 5) • LEMMA 2. At least two objects in P have the distance rPto the min-max-center of P. • LEMMA 3. For any two points x and y on the road network and a set P of objects, md(x, P) ≤ md(y, P) + x, y. For Pruning :- • THEOREM 1. Let pi ∈ P, then md(pi, P)/2 ≤ rP≤md(pi, P). If the min-max-center is on the edge [va, vb], rPis bounded from below by (md(va)+md(vb)−[va, vb])/2 and bounded from above by the smaller of md(va) + [va, vb] and md(vb) +[va, vb].

  10. Road Network Partitioning LEMMA 5. The bitwise-OR of the labels of a set of partition Si (1 ≤ i ≤ n) represents the label of the smallest partition (Scombined) enclosing all Si.

  11. LEMMA 6. The pairwise distance computation is strictly restrained to the partition where both objects are located. If all the objects in set P are inside a partition S, then the max-pairwise-distance of P is no larger than dia(S). • LEMMA 7. If all the objects in set P are inside partition S, then MSC and MMC of P are also inside partition S.

  12. Constraint Evaluation 1. The max-pairwise-distance of P is bounded from above by dia(S). 2. The min-sum-distance of P is bounded from above by (n − 1)dia(S). 3. The min-max-distance of P is bounded from above by dia(S). 4. The max-pairwise-distance of P is bounded from below by max(pdist(Si, Sj)) (1 ≤ i, j ≤ n) . 5. The min-sum-distance of P is bounded from below by P1≤i≤⌊n/2⌋ pdist(S2i−1, S2i) 6. The min-max-distance of P is bounded from below by max(pdist(Si, Sj))/2.

  13. Algorithms :-

  14. Matching with motion plan Vector <route, velocity> as the motion plan • Given a motion plan and a start point on the road network, future constraint matches can be predicted, and historic matches can be computed.

  15. Experiments and Results

  16. Related Work • For road network query processing, Cho et al. and Kolahdouzanet al. proposed the UNICONS and V N3 algorithms for evaluating kNN and continuous kNN queries (CNN) in road networks • Papadiaset al.studied nearest neighbor, range search closest pairs query and e-Distance joins in road networks.

  17. Conclusion • Proximity relations and location constraints specify whether a given set of moving objects are in a specific constellation in road network space • Query processing algorithms for computing the proximity were developed • Experimental evaluations based on real data sets showed that, with all optimizations combined , the total processing overhead is reduced by more than 95%.

  18. References • K. Mouratidis et al. Continuous Nearest Neighbor Monitoring in Road Networks. In VLDB, 2006. • D. Papadias, J. Zhang, N. Mamoulis, and Y. Tao. Query Processing in Spatial Network Databases. In VLDB, 2003. • H. Samet, J. Sankaranarayanan, and H. Alborzi. Scalable network distance browsing in spatial databases. In SIGMOD, 2008. • D. B. West. Introduction to Graph Theory. Prentice Hall, 1996. • K.-L. Wu et al. Efficient Processing of Continual Range Queries for Location-Aware Mobile Services. ISF’05. • Z. Xu. Efficient Location Constraint Processing For Location-aware Computing. Ph.D. Thesis, Univ. of Toronto, 2009.

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