Generating paths and cuts in multi-pole (Di)graphs

Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Leonid Khachiyan, Kazuhisa Makino

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Let G = (V, E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of (source-sink) pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. For directed graphs both of these problems are NP-hard. We also give a polynomial delay algorithm for enumerating minimal sets of arcs connecting respectively two given nodes S1 and S2 to a given vertex t1, and each vertex of a given subset of vertices T2.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsJirí Fiala, Jan Kratochvíl, Vá clav Koubek
PublisherSpringer Verlag
Pages298-309
Number of pages12
Volume3153
ISBN (Electronic)3540228233, 9783540228233
DOIs
StatePublished - Jan 1 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3153

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Boros, E., Elbassioni, K., Gurvich, V., Khachiyan, L., & Makino, K. (2004). Generating paths and cuts in multi-pole (Di)graphs. In J. Fiala, J. Kratochvíl, & V. C. Koubek (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3153, pp. 298-309). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3153). Springer Verlag. https://doi.org/10.1007/978-3-540-28629-5_21