A $(k + 3)/2$-approximation algorithm for monotone submodular maximization over a $k$-exchange system

TL;DR

This paper presents a deterministic local search algorithm that achieves a b1(k+3)/2b1 approximation ratio for maximizing monotone submodular functions over k-exchange systems, extending previous linear maximization results.

Contribution

It introduces a new non-oblivious local search method with improved approximation ratio for monotone submodular maximization in k-exchange systems.

Findings

Achieves a b1(k+3)/2b1 approximation ratio.

Extends previous linear maximization results to submodular functions.

Provides a deterministic algorithm with theoretical guarantees.

Abstract

We consider the problem of maximizing a monotone submodular function in a $k$-exchange system. These systems, introduced by Feldman et al., generalize the matroid k-parity problem in a wide class of matroids and capture many other combinatorial optimization problems. Feldman et al. show that a simple non-oblivious local search algorithm attains a $(k + 1)/2$ approximation ratio for the problem of linear maximization in a $k$-exchange system. Here, we extend this approach to the case of monotone submodular objective functions. We give a deterministic, non-oblivious local search algorithm that attains an approximation ratio of $(k + 3)/2$ for the problem of maximizing a monotone submodular function in a $k$-exchange system.