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The exact distance to destination in undirected world

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Abstract

Shortest distance queries are essential not only in graph analysis and graph mining tasks but also in database applications, when a large graph needs to be dealt with. Such shortest distance queries are frequently issued by end-users or requested as a subroutine in real applications. For intensive queries on large graphs, it is impractical to compute shortest distances on-line from scratch, and impractical to materialize all-pairs shortest distances. In the literature, 2-hop distance labeling is proposed to index the all-pairs shortest distances. It assigns distance labels to vertices in a large graph in a pre-computing step off-line and then answers shortest distance queries on-line by making use of such distance labels, which avoids exhaustively traversing the large graph when answering queries. However, the existing algorithms to generate 2-hop distance labels are not scalable to large graphs. Finding an optimal 2-hop distance labeling is NP-hard, and heuristic algorithms may generate large size distance labels while still needing to pre-compute all-pairs shortest paths. In this paper, we propose a multi-hop distance labeling approach, which generates a subset of the 2-hop distance labels as index off-line. We can compute the multi-hop distance labels efficiently by avoiding pre-computing all-pairs shortest paths. In addition, our multi-hop distance labeling is small in size to be stored. To answer a shortest distance query between two vertices, we first generate the query-specific small set of 2-hop distance labels for the two vertices based on our multi-hop distance labels stored and compute the shortest distance between the two vertices based on the 2-hop distance labels generated on-line. We conducted extensive performance studies on large real graphs and confirmed the efficiency of our multi-hop distance labeling scheme.

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References

  1. Arnborg S., Corneil D.G., Proskurowski A.: Complexity of finding embeddings in a k-tree. SIAM J. Algebraic Discret Methods 8(2), 277–284 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barabasi A.-L., Albert R.: Emergence of scaling in random networks. Science. 286, 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  3. Baswana S., Sen S.: Approximate distance oracles for unweighted graphs in expected o(n2) time. ACM Trans. Algorithms 2(4), 557–577 (2006)

    Article  MathSciNet  Google Scholar 

  4. Bodlaender H.L., Koster A.M.C.A: Treewidth computations I. Upper bounds. Inf. Comput. 208(3), 259–275 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chaudhuri S., Zaroliagis C.D.: Shortest paths in digraphs of small treewidth. Part I: Sequential algorithms. Algorithmica. 27(3), 212–226 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Cheng, J., Yu, J.X.: On-line exact shortest distance query processing. In: Proceedings of EDBT’09, pp. 481–492 (2009)

  7. Cohen, E., Halperin, E., Kaplan, H., Zwick, U.: Reachability and distance queries via 2-hop labels. In: Proceedings of SODA’02, pp. 937–946 (2002)

  8. Cormen T.H., Stein C., Rivest R.L., Leiserson C.E.: Introduction to Algorithms. McGraw-Hill Higher Education, USA (2001)

    MATH  Google Scholar 

  9. Das Sarma, A., Gollapudi, S., Najork, M., Panigrahy, R.: A sketch-based distance oracle for web-scale graphs. In: Proceedings of WSDM’10, pp. 401–410 (2010)

  10. Fan W., Ma S., Tang N., Wu Y., Wu Y.: Graph pattern matching: from intractable to polynomial time. PVLDB 3(1), 264–275 (2010)

    Google Scholar 

  11. Gavoille, C., Peleg, D., Perennes, S., Raz, R.: Distance labeling in graphs. In: Proceedings of SODA’01, pp. 210–219 (2001)

  12. Geisberger, R., Sanders, P., Schultes, D., Delling, D.: Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In: WEA, pp. 319–333. (2008)

  13. Gou, G., Chirkova, R.: Efficient algorithms for exact ranked twig-pattern matching over graphs. In: Proceedings of SIGMOD’08, pp. 581–594 (2008)

  14. Jin, R., Xiang, Y., Ruan, N., Fuhry, D.: 3-hop: a high-compression indexing scheme for reachability query. In: Proceedings of SIGMOD’09, pp. 813–826 (2009)

  15. Jin, R., Xiang, Y., Ruan, N., Wang, H.: Efficiently answering reachability queries on very large directed graphs. In: Proceedings of SIGMOD’08, pp. 595–608 (2008)

  16. Katz, M., Katz, N.A., Peleg, D.: Distance labeling schemes for well-separated graph classes. In: Proceedings of STACS’00, pp. 516–528 (2000)

  17. Li, F., Cheng, D., Hadjieleftheriou, M., Kollios, G., Teng, S.-H.: On trip planning queries in spatial databases. In: Proceedings of SSTD’05, pp. 273–290 (2005)

  18. Liu, L., Wong, R.C.-W.: Finding shortest path on land surface. In: Proceedings of SIGMOD’11, pp. 433–444 (2011)

  19. Peleg D.: Proximity-preserving labeling schemes. J. Graph Theory 33(3), 167–176 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rahman S.A., Advani P., Schunk R., Schrader R., Schomburg D.: Metabolic pathway analysis web service (pathway hunter tool at cubic). Bioinformatics 21(7), 1189–1193 (2005)

    Article  Google Scholar 

  21. Rice M., Tsotras V.J.: Graph indexing of road networks for shortest path queries with label restrictions. PVLDB 4(2), 69–80 (2010)

    Google Scholar 

  22. Robertson N., Seymour P.D.: Graph minors. iii. Planar tree-width. J. Comb. Theory Ser. B 36(1), 49–64 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  23. Sankaranarayanan J., Samet H.: Roads belong in databases. IEEE Data Eng. Bull. 33(2), 4–11 (2010)

    Google Scholar 

  24. Schenkel, R., Theobald, A., Weikum, G.: Hopi: an efficient connection index for complex xml document collections. In: Proceedings of EDBT’04, pp. 237–255 (2004)

  25. Schenkel, R., Theobald, A., Weikum, G.: Efficient creation and incremental maintenance of the hopi index for complex xml document collections. In: Proceedings of ICDE’05, pp. 360–371 (2005)

  26. Sommer, C., Verbin, E., Yu, W.: Distance oracles for sparse graphs. In: Proceedings of FOCS’09, pp. 703–712 (2009)

  27. Thorup, M., Zwick, U.: Approximate distance oracles. In: Proceedings of STOC’01, pp. 183–192 (2001)

  28. van Schaik, S.J., de Moor, O.: A memory efficient reachability data structure through bit vector compression. In: Proceedings of SIGMOD’11, pp. 913–924 (2011)

  29. Wei, F.: TEDI: efficient shortest path query answering on graphs. In: Proceedings of SIGMOD’10, pp. 99–110 (2010)

  30. Xiao, Y., Wu, W., Pei, J., Wang, W., He, Z.: Efficiently indexing shortest paths by exploiting symmetry in graphs. In: Proceedings of EDBT’09, pp. 493–504 (2009)

  31. Yildirim H., Chaoji V., Zaki M.J.: Grail: scalable reachability index for large graphs. PVLDB 3(1), 276–284 (2010)

    Google Scholar 

  32. Yu, J.X., Qin, L., Chang, L.: Keyword Search in Databases. Morgan & Claypool Publishers, San Francisco (2010)

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Authors and Affiliations

  1. The Chinese University of Hong Kong, Hong Kong, China

    Lijun Chang, Jeffrey Xu Yu, Lu Qin, Hong Cheng & Miao Qiao

Authors
  1. Lijun Chang
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  2. Jeffrey Xu Yu
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  3. Lu Qin
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  4. Hong Cheng
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  5. Miao Qiao
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Correspondence to Jeffrey Xu Yu.

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Chang, L., Yu, J.X., Qin, L. et al. The exact distance to destination in undirected world. The VLDB Journal 21, 869–888 (2012). https://doi.org/10.1007/s00778-012-0274-x

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  • DOI: https://doi.org/10.1007/s00778-012-0274-x

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