Linear programming to approximate quadratic 0-1 maximization problems

Abstract

Many authors have used the continuous relaxation of linear formulations of quadratic 0-1 optimization problems subject to linear constraints in order to obtain a bound of the optimal value by linear programming. But usually, optimal solutions are non-integer vectors, and thus are not feasible for the 0-1 problem. In this paper, we propose a based linear programming scheme to try to build ε-approximate polynomial time algorithms for any quadratic 0-1 maximization problems subject to linear constraints. By using this scheme, we obtain ε-approximate polynomial-time algorithms for several basic problems : the maximization of an unconstrained quadratic posiform, an assignment problem which contains k-max-cut as a particular case, k-max-cut, the k-cluster problem on bipartite graphs, and the bipartitioning problem (max-cut with a set of cardinal k).