Generating all maximal induced subgraphs for hereditary and connected-hereditary graph properties

Sara Cohen*, Benny Kimelfeld, Yehoshua Sagiv

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

This paper investigates a graph enumeration problem, called the maximalP -subgraphs problem, where P is a hereditary or connected-hereditary graph property. Formally, given a graph G, the maximal P-subgraphs problem is to generate all maximal induced subgraphs of G that satisfy P. This problem differs from the well-known node-deletion problem, studied by Yannakakis and Lewis [J. Lewis, On the complexity of the maximum subgraph problem, in: Proc. 10th Annual ACM Symposium on Theory of Computing, ACM Press, New York, USA, 1978, pp. 265-274; M. Yannakakis, Node- and edge-deletion NP-complete problems, in: Proc. 10th Annual ACM Symposium on Theory of Computing, ACM Press, New York, USA, 1978, pp. 253-264; J. Lewis, M. Yannakakis, The node-deletion problem for hereditary properties is NP-complete, J. Comput. System Sci. 20 (2) (1980) 219-230]. In the maximal P-subgraphs problem, the goal is to produce all (locally) maximal subgraphs of a graph that have property P, whereas in the node-deletion problem, the goal is to find a single (globally) maximum size subgraph with property P. Algorithms are presented that reduce the maximal P-subgraphs problem to an input-restricted version of this problem. These algorithms imply that when attempting to efficiently solve the maximal P-subgraphs problem for a specific P, it is sufficient to solve the restricted case. The main contributions of this paper are characterizations of when the maximal P-subgraphs problem is in a complexity class C (e.g., polynomial delay, total polynomial time).

Original languageAmerican English
Pages (from-to)1147-1159
Number of pages13
JournalJournal of Computer and System Sciences
Volume74
Issue number7
DOIs
StatePublished - Nov 2008

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (S. Cohen), [email protected] (B. Kimelfeld), [email protected] (Y. Sagiv). 1 Sara Cohen was partially supported by The Israel Science Foundation (Grant 1032/05). 2 Benny Kimelfeld and Yehoshua Sagiv were partially supported by The Israel Science Foundation (Grant 893/05).

Keywords

  • Complexity classes
  • Enumeration
  • Graph properties
  • Hereditary properties
  • Maximal subgraphs

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