A comment on "Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid"

TL;DR

This paper critiques a previous work by providing a counterexample that challenges the claimed performance guarantees of a greedy algorithm for supermodular set function minimization on comatroids.

Contribution

It identifies a flaw in the original proof and clarifies the limitations of the previous performance guarantee claims.

Findings

Counterexample disproves the original performance guarantee

Analysis pinpoints the proof error in the prior work

Highlights the need for revised guarantees in this context

Abstract

We provide a counterexample to the performance guarantee obtained in the paper "Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid", which was published in Volume 171 of the European Journal of Operational Research. We comment on where this error originates from in the proof of the main theorem.