An Improved Greedy Curvature Bound in Finite-Horizon String Optimization with Application to a Sensor Coverage Problem

TL;DR

This paper introduces an improved greedy curvature bound for finite-horizon string optimization problems, outperforming previous bounds in computational efficiency and effectiveness, with applications demonstrated in sensor coverage.

Contribution

It presents a novel, computationally efficient greedy curvature bound for string submodular optimization, surpassing existing bounds in performance guarantees.

Findings

The new bound is tighter than previous curvature bounds.

The proposed method reduces computational complexity.

Application to sensor coverage demonstrates practical effectiveness.

Abstract

We study the optimization problem of choosing strings of finite length to maximize string submodular functions on string matroids, which is a broader class of problems than maximizing set submodular functions on set matroids. We provide a lower bound for the performance of the greedy algorithm in our problem, and then prove that our bound is superior to the greedy curvature bound of Conforti and Cornuejols. Our bound has lower computational complexity than most previously proposed curvature bounds. Finally, we demonstrate the strength of our result on a sensor coverage problem.