Abstract.
Given an undirected graph G=(V,E) with |V|=n and an integer k between 0 and n, the maximization graph partition (MAX-GP) problem is to determine a subset S⊂V of k nodes such that an objective function w(S) is maximized. The MAX-GP problem can be formulated as a binary quadratic program and it is NP-hard. Semidefinite programming (SDP) relaxations of such quadratic programs have been used to design approximation algorithms with guaranteed performance ratios for various MAX-GP problems. Based on several earlier results, we present an improved rounding method using an SDP relaxation, and establish improved approximation ratios for several MAX-GP problems, including Dense-Subgraph, Max-Cut, Max-Not-Cut, and Max-Vertex-Cover.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: March 10, 2000 / Accepted: July 13, 2001¶Published online February 14, 2002
Rights and permissions
About this article
Cite this article
Han, Q., Ye, Y. & Zhang, J. An improved rounding method and semidefinite programming relaxation for graph partition. Math. Program. 92, 509–535 (2002). https://doi.org/10.1007/s101070100288
Issue Date:
DOI: https://doi.org/10.1007/s101070100288