Branch-and-price-and-cut on the clique partitioning problem with minimum clique size requirement

Authors:
Xiaoyun Ji;John E. Mitchell
Affiliations:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Venue:
Discrete Optimization
Year:
2007

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Abstract

Given a complete graph K"n=(V,E) with edge weight c"e on each edge, we consider the problem of partitioning the vertices of graph K"n into subcliques that have at least S vertices, so as to minimize the total weight of the edges that have both endpoints in the same subclique. In this paper, we consider using the branch-and-price method to solve the problem. We demonstrate the necessity of cutting planes for this problem and suggest effective ways of adding cutting planes in the branch-and-price framework. The NP hard pricing problem is solved as an integer programming problem. We present computational results on large randomly generated problems.