Submodular Cost Submodular Cover with an Approximate Oracle

TL;DR

This paper addresses the challenge of minimizing submodular costs to achieve a benefit threshold when only approximate access to the benefit function is available, providing new approximation guarantees and empirical insights.

Contribution

It introduces two new approximation ratios for the submodular cover problem with an approximate oracle and demonstrates their practical relevance through a social network case study.

Findings

Two incomparable approximation ratios derived for the problem.

Empirical relevance of the ratios shown in social network case study.

Approximate oracle access impacts the effectiveness of greedy algorithms.

Abstract

In this work, we study the Submodular Cost Submodular Cover problem, which is to minimize the submodular cost required to ensure that the submodular benefit function exceeds a given threshold. Existing approximation ratios for the greedy algorithm assume a value oracle to the benefit function. However, access to a value oracle is not a realistic assumption for many applications of this problem, where the benefit function is difficult to compute. We present two incomparable approximation ratios for this problem with an approximate value oracle and demonstrate that the ratios take on empirically relevant values through a case study with the Influence Threshold problem in online social networks.