Generating Paths and Cuts in Multi-pole (Di)graphs

  • Endre Boros
  • Khaled Elbassioni
  • Vladimir Gurvich
  • Leonid Khachiyan
  • Kazuhisa Makino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3153)


Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set \(\mathcal P\) 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 \(\mathcal P\). 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 s 1 and s 2 to a given vertex t 1, and each vertex of a given subset of vertices T 2.


Span Tree Undirected Graph Steiner Tree Conjunctive Normal Form Network Reliability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Endre Boros
    • 1
  • Khaled Elbassioni
    • 1
  • Vladimir Gurvich
    • 1
  • Leonid Khachiyan
    • 2
  • Kazuhisa Makino
    • 3
  1. 1.RUTCORRutgers UniversityPiscatawayUSA
  2. 2.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  3. 3.Division of Systems Science, Graduate School of Engineering ScienceOsaka UniversityToyonaka, OsakaJapan

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