Branch-and-Price-and-Cut on the Clique Partition Problem with Minimum Clique Size Requirement

Download the paper, in pdf.

Authors:

Xiaoyun Ji
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
jix at rpi.edu

John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
mitchj at rpi.edu

Citation details:

Discrete Optimization, 4 (1), 2007, pages 87-102.

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.

Download the paper, in pdf.

Return to my list of papers.