Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

TL;DR

This paper introduces a straightforward greedy D-approximation algorithm applicable to a broad class of covering problems with submodular, non-decreasing objectives and arbitrary covering constraints involving at most D variables, generalizing prior algorithms.

Contribution

It presents a novel greedy approximation algorithm that works for any covering problem with submodular costs and arbitrary constraints involving up to D variables, extending previous methods.

Findings

The algorithm achieves a D-approximation ratio for the general class of problems.

It generalizes existing algorithms for specific covering and caching problems.

The approach simplifies solving complex covering problems with submodular objectives.

Abstract

This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards) covering constraints, each of which constrains at most D variables of the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm generalizes previous approximation algorithms for fundamental covering problems and online paging and caching problems.