An exact algorithm for graph partitioning

• 成果类型: Article
• 署名作者: Hager, William W.; Phan, Dzung T.; Zhang, Hongchao
• 署名单位: State University System of Florida; University of Florida; International Business Machines (IBM); IBM USA; Louisiana State University System; Louisiana State University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0503-x
• 发表日期: 2013
• 页码: 531-556
• 关键词: irregular graphs; optimization; DECOMPOSITION; scheme

摘要

An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained by decomposing the objective function into convex and concave parts and replacing the concave part by an affine underestimate. It is shown that the best affine underestimate can be expressed in terms of the center and the radius of the smallest sphere containing the feasible set. The concave term is obtained either by a constant diagonal shift associated with the smallest eigenvalue of the objective function Hessian, or by a diagonal shift obtained by solving a semidefinite programming problem. Numerical results show that the proposed algorithm is competitive with state-of-the-art graph partitioning codes.