A note on maximizing a submodular set function subject to a knapsack constraint

Abstract

A note on maximizing a submodular set function subject to a knapsack constraint was presented. An (1-e-1)-approximation algorithm for maximizing a nondecreasing submodular set function was obtained. This algorithm required O(n5) function value computations. The algorithm enumerated all feasible solutions of cardinality one or two.