Annals of Discrete Mathematics (11) - Studies on Graphs and Discrete Programming

Abstract

We consider integer programming formulations of problems that involve the maximization of submodular functions. A location problem and a 0–1 quadratic program are well-known special cases. We give a constraint generation algorithm and a branch-and-bound algorithm that uses linear programming relaxations. These algorithms are familiar ones except for their particular selections of starting constraints, subproblems and partitioning rules. The algorithms use greedy heuristics to produce feasible solutions, which, in turn, are used to generate upper bounds. The novel features of the algorithms are the performance guarantees they provide on the ratio of lower to upper bounds on the optimal value.