Generating Paths and Cuts in Multi-pole (Di)graphs
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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.
KeywordsSpan Tree Undirected Graph Steiner Tree Conjunctive Normal Form Network Reliability
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