The maximum common edge subgraph problem: A polyhedral investigation. Bahiense, L., Manić, G., Piva, B., & de Souza, C. C. Discrete Appl Math, 160(18):2523 - 2541, 2012.
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In the Maximum Common Edge Subgraph Problem (MCES), given two graphs G and H with the same number of vertices, one has to find a common subgraph of G and H (not necessarily induced) with the maximum number of edges. This problem arises in parallel programming environments, and was first defined in?Bokhari (1981) [2]. This paper presents a new integer programming formulation for the MCES and a polyhedral study of this model. Several classes of valid inequalities are identified, most of which are shown to define facets. These findings were incorporated into a branch&cut algorithm we implemented. Experimental results with this algorithm are reported.
@Article{bahiense12maximum,
  author    = {Laura Bahiense and Gordana Mani\'c and Breno Piva and Cid C. de Souza},
  title     = {The maximum common edge subgraph problem: A polyhedral investigation},
  journal   = {Discrete Appl Math},
  year      = {2012},
  volume    = {160},
  number    = {18},
  pages     = {2523 - 2541},
  abstract  = {In the Maximum Common Edge Subgraph Problem (MCES), given two graphs G and H with the same number of vertices, one has to find a common subgraph of G and H (not necessarily induced) with the maximum number of edges. This problem arises in parallel programming environments, and was first defined in?Bokhari (1981) [2]. This paper presents a new integer programming formulation for the MCES and a polyhedral study of this model. Several classes of valid inequalities are identified, most of which are shown to define facets. These findings were incorporated into a branch&cut algorithm we implemented. Experimental results with this algorithm are reported.},
  doi       = {10.1016/j.dam.2012.01.026},
  keywords  = {Maximum common subgraph problem, Graph isomorphism, Polyhedral combinatorics, Branch&cut algorithm},
  owner     = {Sebastian},
  timestamp = {2019.08.04},
}

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