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Finding reliable subgraphs from large probabilistic graphs

  • Petteri Hintsanen
  • Hannu Toivonen
Article

Abstract

Reliable subgraphs can be used, for example, to find and rank nontrivial links between given vertices, to concisely visualize large graphs, or to reduce the size of input for computationally demanding graph algorithms. We propose two new heuristics for solving the most reliable subgraph extraction problem on large, undirected probabilistic graphs. Such a problem is specified by a probabilistic graph G subject to random edge failures, a set of terminal vertices, and an integer K. The objective is to remove K edges from G such that the probability of connecting the terminals in the remaining subgraph is maximized. We provide some technical details and a rough analysis of the proposed algorithms. The practical performance of the methods is evaluated on real probabilistic graphs from the biological domain. The results indicate that the methods scale much better to large input graphs, both computationally and in terms of the quality of the result.

Keywords

Link discovery and analysis Graph mining Graph visualization Reliability 

References

  1. Birnbaum ZW (1969) On the importance of different components in a multicomponent system. Multivar Anal II:581–592Google Scholar
  2. Bryant RE (1986) Graph-based algorithms for boolean function manipulation. IEEE Trans Comput 35: 677–691zbMATHCrossRefGoogle Scholar
  3. Colbourn CJ (1987) The combinatorics of network reliability. Oxford University Press, OxfordGoogle Scholar
  4. De Raedt L, Kersting K, Kimmig A, Revoredo K, Toivonen H (2008) Compressing probabilistic Prolog programs. Mach Learn 70: 151–168CrossRefGoogle Scholar
  5. Duffin RJ (1965) Topology of series–parallel networks. J Math Anal Appl 10: 303–318zbMATHCrossRefMathSciNetGoogle Scholar
  6. Eppstein D (1998) Finding the k shortest paths. SIAM J Comput 28: 652–673zbMATHCrossRefMathSciNetGoogle Scholar
  7. Faloutsos C, McCurley KS, Tomkins A (2004) Fast discovery of connection subgraphs. In: Proceedings of the 10th ACM SIGKDD international conference on knowledge discovery and data mining, pp 118–127Google Scholar
  8. Hershberger J, Maxel M, Suri S (2007) Finding the k shortest simple paths: a new algorithm and its implementation. ACM Trans Algorithms 3: 45CrossRefMathSciNetGoogle Scholar
  9. Hintsanen P (2007) The most reliable subgraph problem. In: Proceedings of the 11th European conference on principles and practice of knowledge discovery in databases, pp 471–478Google Scholar
  10. Lawler EL (1972) A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem. Manage Sci 18: 401–405zbMATHMathSciNetCrossRefGoogle Scholar
  11. Roditty L (2007) On the k-simple shortest paths problem in weighted directed graphs. In: Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms, pp 920–928Google Scholar
  12. Sevon P, Eronen L, Hintsanen P, Kulovesi K, Toivonen H (2006) Link discovery in graphs derived from biological databases. In: Proceedings of data integration in the life sciences. Third international workshop, pp 35–49Google Scholar
  13. Valdes J, Tarjan RE, Lawler EL (1982) The recognition of series–parallel digraphs. SIAM J Comput 11: 298–313zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Helsinki Institute for Information Technology, Department of Computer ScienceUniversity of HelsinkiHelsinkiFinland

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