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Edge cover by connected bipartite subgraphs

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Abstract

We consider the problem of covering the edge set of an unweighted, undirected graph with the minimum number of connected bipartite subgraphs (where the subgraphs are not necessarily bicliques). We show that this is an NP-hard problem, provide lower bounds through an integer programming formulation, propose several constructive heuristics and a local search, and discuss computational results. Finally, we consider a constrained variant of the problem which we show to be NP-hard, and provide an integer programming formulation for the variant.

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Authors and Affiliations

  1. LIX, École Polytechnique, 91128, Palaiseau, France

    Leo Liberti

  2. ESSEC, Av. Bernard Hirsch, BP105, 95021, Cergy Pontoise, France

    Laurent Alfandari

  3. CEDRIC, CNAM, 292 rue St. Martin, 75141, Paris, France

    Marie-Christine Plateau

Authors
  1. Leo Liberti
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  2. Laurent Alfandari
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  3. Marie-Christine Plateau
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Correspondence to Leo Liberti.

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Liberti, L., Alfandari, L. & Plateau, MC. Edge cover by connected bipartite subgraphs. Ann Oper Res 188, 307–329 (2011). https://doi.org/10.1007/s10479-009-0533-4

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  • DOI: https://doi.org/10.1007/s10479-009-0533-4

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