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

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.

• Type: Conference
• Year: 2004
• Where: MFCS
• Authors: Endre Boros, Khaled M. Elbassioni, Vladimir Gurvich, Leonid Khachiyan, Kazuhisa Makino
• Keywords: Incremental Polynomial Time, MFCS 2004, Minimal Subsets, Polynomial Delay Algorithm