Efficient processing of distance queries in large graphs: a vertex cover approach

We propose a novel disk-based index for processing single-source shortest path or distance queries. The index is useful in a wide range of important applications (e.g., network analysis, routing planning, etc.). Our index is a tree-structured index constructed based on the concept of vertex cover. We propose an I/O-efficient algorithm to construct the index when the input graph is too large to fit in main memory. We give detailed analysis of I/O and CPU complexity for both index construction and query processing, and verify the efficiency of our index for query processing in massive real-world graphs.

[1]  T. Valente,et al.  Integration and radiality: Measuring the extent of an individual's connectedness and reachability in a network , 1998 .

[2]  Kurt Mehlhorn,et al.  External-Memory Breadth-First Search with Sublinear I/O , 2002, ESA.

[3]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[4]  Marc Najork,et al.  Breadth-first crawling yields high-quality pages , 2001, WWW '01.

[6]  David Eppstein,et al.  Fast approximation of centrality , 2000, SODA '01.

[7]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[8]  Jonathan S. Turner,et al.  Approximation Algorithms for the Shortest Common Superstring Problem , 1989, Inf. Comput..

[9]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[10]  James E. Morrow.  The University of Washington , 2004 .

[11]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[12]  Silvio Micali,et al.  An O(v|v| c |E|) algoithm for finding maximum matching in general graphs , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[13]  Ulrich Meyer,et al.  Design and Implementation of a Practical I/O-efficient Shortest Paths Algorithm , 2009, ALENEX.

[14]  Vijay Kumar,et al.  Improved algorithms and data structures for solving graph problems in external memory , 1996, Proceedings of SPDP '96: 8th IEEE Symposium on Parallel and Distributed Processing.

[15]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[16]  T.R. Coffman,et al.  Sensitivity of social network analysis metrics to observation noise , 2004, 2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720).

[17]  Ulrich Meyer,et al.  I/O-Efficient Undirected Shortest Paths with Unbounded Edge Lengths , 2006, ESA.

[18]  Suresh Venkatasubramanian,et al.  On external memory graph traversal , 2000, SODA '00.

[19]  Amos Fiat,et al.  Highway dimension, shortest paths, and provably efficient algorithms , 2010, SODA '10.

[20]  Jeffrey Xu Yu,et al.  Finding maximal cliques in massive networks by H*-graph , 2010, SIGMOD Conference.

[21]  Alok Aggarwal,et al.  The input/output complexity of sorting and related problems , 1988, CACM.

[22]  S. Safra,et al.  On the hardness of approximating minimum vertex cover , 2005 .

[23]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[24]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[25]  Ulrich Meyer,et al.  I/O-Efficient Undirected Shortest Paths , 2003, ESA.

[26]  Ulrich Meyer,et al.  Via Detours to I/O-Efficient Shortest Paths , 2009, Efficient Algorithms.

[27]  Kamesh Munagala,et al.  I/O-complexity of graph algorithms , 1999, SODA '99.

[28]  Ulrich Meyer,et al.  Improved External Memory BFS Implementation , 2007, ALENEX.

[29]  Fang Wei-Kleiner,et al.  TEDI: Efficient Shortest Path Query Answering on Graphs , 2010, Graph Data Management.

[30]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[31]  Jian Pei,et al.  Efficiently indexing shortest paths by exploiting symmetry in graphs , 2009, EDBT '09.

[32]  Piotr Indyk,et al.  Fast estimation of diameter and shortest paths (without matrix multiplication) , 1996, SODA '96.

[33]  Ulrich Meyer,et al.  A computational study of external-memory BFS algorithms , 2006, SODA '06.

[34]  Brighten Godfrey,et al.  Approximate distance queries and compact routing in sparse graphs , 2011, 2011 Proceedings IEEE INFOCOM.

[35]  T.R. Coffman,et al.  Dynamic classification of groups through social network analysis and HMMs , 2004, 2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720).

[36]  W. K. George,et al.  University of Illinois at Urbana-Champain , 1997 .

[37]  A. Shimbel.  Structural parameters of communication networks , 1953 .

[38]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .