ABSTRACT
We propose two dynamic indexing schemes for shortest-path and distance queries on large time-evolving graphs, which are useful in a wide range of important applications such as real-time network-aware search and network evolution analysis. To the best of our knowledge, these methods are the first practical exact indexing methods to efficiently process distance queries and dynamic graph updates. We first propose a dynamic indexing scheme for queries on the last snapshot. The scalability and efficiency of its offline indexing algorithm and query algorithm are competitive even with previous static methods. Meanwhile, the method is dynamic, that is, it can incrementally update indices as the graph changes over time. Then, we further design another dynamic indexing scheme that can also answer two kinds of historical queries with regard to not only the latest snapshot but also previous snapshots.
Through extensive experiments on real and synthetic evolving networks, we show the scalability and efficiency of our methods. Specifically, they can construct indices from large graphs with millions of vertices, answer queries in microseconds, and update indices in milliseconds.
- I. Abraham, D. Delling, A. V. Goldberg, and R. F. Werneck. Hierarchical hub labelings for shortest paths. In ESA, pages 24--35. 2012. Google ScholarDigital Library
- F. Aidouni, M. Latapy, and C. Magnien. Ten weeks in the life of an edonkey server. In IPDPS, pages 1--5, 2009. Google ScholarDigital Library
- T. Akiba, Y. Iwata, K. Kawarabayashi, and Y. Kawata. Fast shortest-path distance queries on road networks by pruned highway labeling. In ALENEX, pages 147--154, 2014.Google ScholarDigital Library
- T. Akiba, Y. Iwata, and Y. Yoshida. Fast exact shortest-path distance queries on large networks by pruned landmark labeling. In SIGMOD, pages 349--360, 2013. Google ScholarDigital Library
- T. Akiba, C. Sommer, and K. Kawarabayashi. Shortest-path queries for complex networks: exploiting low tree-width outside the core. In EDBT, pages 144--155, 2012. Google ScholarDigital Library
- L. Backstrom, D. Huttenlocher, J. Kleinberg, and X. Lan. Group formation in large social networks: membership, growth, and evolution. In KDD, pages 44--54, 2006. Google ScholarDigital Library
- A.-L. Barabasi. The origin of bursts and heavy tails in human dynamics. Nature, 435:207--211, 2005.Google ScholarCross Ref
- A.-L. Barabási and R. Albert. Emergence of scaling in random networks. Science, 286(5439):509--512, 1999.Google ScholarCross Ref
- S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. Hwang. Complex networks: Structure and dynamics. Physics reports, 424(4-5):175--308, 2006.Google ScholarCross Ref
- D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Network robustness and fragility: Percolation on random graphs. Physical Review Letters, 85:5468--5471, 2000.Google ScholarCross Ref
- J. Cheng and J. X. Yu. On-line exact shortest distance query processing. In EDBT, pages 481--492, 2009. Google ScholarDigital Library
- E. Cohen, E. Halperin, H. Kaplan, and U. Zwick. Reachability and distance queries via 2-hop labels. In SODA, pages 937--946, 2002. Google ScholarDigital Library
- A. Das Sarma, S. Gollapudi, M. Najork, and R. Panigrahy. A sketch-based distance oracle for web-scale graphs. In WSDM, 2010. Google ScholarDigital Library
- S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin. Structure of growing networks with preferential linking. Phys. Rev. Lett., 85:4633--4636, 2000.Google ScholarCross Ref
- A. W.-C. Fu, H. Wu, J. Cheng, S. Chu, and R. C.-W. Wong. Is-label: an independent-set based labeling scheme for point-to-point distance querying on large graphs. PVLDB, 6(6):457--468, 2013. Google ScholarDigital Library
- R. Jin, N. Ruan, Y. Xiang, and V. Lee. A highway-centric labeling approach for answering distance queries on large sparse graphs. In SIGMOD, pages 445--456, 2012. Google ScholarDigital Library
- D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the spread of influence through a social network. In KDD, pages 137--146, 2003. Google ScholarDigital Library
- B. Klimt and Y. Yang. The enron corpus: A new dataset for email classification research. In ECML, volume 3201 of LNCS, pages 217--226. 2004.Google Scholar
- J. Leskovec, J. Kleinberg, and C. Faloutsos. Graph evolution: Densification and shrinking diameters. TKDD, 1(1), 2007. Google ScholarDigital Library
- P. Massa and P. Avesani. Controversial users demand local trust metrics: an experimental study on epinions.com community. In AAAI, pages 121--126, 2005. Google ScholarDigital Library
- A. Mislove. Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems. PhD thesis, Rice University, 2009. Google ScholarDigital Library
- M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64(2):026118 1--17, 2001.Google ScholarCross Ref
- R. Pastor-Satorras and A. Vespignani. Evolution and structure of the Internet: A statistical physics approach. Cambridge University Press, 2004. Google ScholarDigital Library
- M. Potamias, F. Bonchi, C. Castillo, and A. Gionis. Fast shortest path distance estimation in large networks. In CIKM, pages 867--876, 2009. Google ScholarDigital Library
- M. Qiao, H. Cheng, L. Chang, and J. X. Yu. Approximate shortest distance computing: A query-dependent local landmark scheme. In ICDE, pages 462--473, 2012. Google ScholarDigital Library
- S. A. Rahman, P. Advani, R. Schunk, R. Schrader, and D. Schomburg. Metabolic pathway analysis web service (pathway hunter tool at cubic). Bioinformatics, 21(7):1189--1193, 2005. Google ScholarDigital Library
- S. A. Rahman and D. Schomburg. Observing local and global properties of metabolic pathways: 'load points' and 'choke points' in the metabolic networks. Bioinformatics, 22(14):1767--1774, 2006. Google ScholarDigital Library
- N. Robertson and P. D. Seymour. Graph minors. III. Planar tree-width. J. Comb. Theory, Ser. B, 36(1):49--64, 1984.Google ScholarCross Ref
- L. Tang and M. Crovella. Virtual landmarks for the internet. In SIGCOMM, pages 143--152, 2003. Google ScholarDigital Library
- K. Tretyakov, A. Armas-Cervantes, L. García-Bañuelos, J. Vilo, and M. Dumas. Fast fully dynamic landmark-based estimation of shortest path distances in very large graphs. In CIKM, pages 1785--1794, 2011. Google ScholarDigital Library
- A. Ukkonen, C. Castillo, D. Donato, and A. Gionis. Searching the wikipedia with contextual information. In CIKM, pages 1351--1352, 2008. Google ScholarDigital Library
- M. V. Vieira, B. M. Fonseca, R. Damazio, P. B. Golgher, D. d. C. Reis, and B. Ribeiro-Neto. Efficient search ranking in social networks. In CIKM, pages 563--572, 2007. Google ScholarDigital Library
- B. Viswanath, A. Mislove, M. Cha, and K. P. Gummadi. On the evolution of user interaction in facebook. In WOSN, pages 37--42, 2009. Google ScholarDigital Library
- F. Wei. Tedi: efficient shortest path query answering on graphs. In SIGMOD, pages 99--110, 2010. Google ScholarDigital Library
- S. A. Yahia, M. Benedikt, L. V. S. Lakshmanan, and J. Stoyanovich. Efficient network aware search in collaborative tagging sites. PVLDB, 1(1):710--721, 2008. Google ScholarDigital Library
- Y. Yano, T. Akiba, Y. Iwata, and Y. Yoshida. Fast and scalable reachability queries on graphs by pruned labeling with landmarks and paths. In CIKM, pages 1601--1606, 2013. Google ScholarDigital Library
Index Terms
- Dynamic and historical shortest-path distance queries on large evolving networks by pruned landmark labeling
Recommendations
Fast exact shortest-path distance queries on large networks by pruned landmark labeling
SIGMOD '13: Proceedings of the 2013 ACM SIGMOD International Conference on Management of DataWe propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient at first ...
Fast fully dynamic labelling for distance queries
AbstractFinding the shortest-path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has explored this problem, most of which is limited to static graphs. Due to the dynamic nature of ...
Shortest Path Tree Computation in Dynamic Graphs
Let G = (V, E, w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G^{\prime} be obtained from G by an application of a set of edge weight updates to G. Let s\in V and let T_{s} and T_{s}^{\prime} be Shortest Path Trees (...
Comments