A GREEDY ALGORITHM FOR MINIMIZING A SEPARABLE CONVEX FUNCTION OVER A FINITE JUMP SYSTEM

Abstract

We present a greedy algorithm for minimizing a separable convex function over a finite jump system (E,f), where E is a nonempty finite set and f is a nonempty finite set of integral points in Z^E satisfying a certain exchange axiom. The concept of jump system was introduced by A. Bouchet and W. H. Cunningham. A jump system is a generalization of an integral bisubmodular polyhedron, an integral polymatroid, a (poly-)pseudomatroid and a delta-matroid, and has combinatorially nice properties. The algorithm starts with an arbitrary feasible solution and a current feasible solution incrementally moves toward an optimal one in a greedy way. We also show that the greedy algorithm terminates after changing an initial feasible solution at most[numerical formula] times, where for each e ∈ E [numerical formula].