A Tighter Analysis of Setcover Greedy Algorithm for Test Set

TL;DR

This paper provides a more precise analysis of the setcover greedy algorithm for test set problems, improving its performance guarantee and establishing a lower bound, thus clarifying its effectiveness relative to the information content heuristic.

Contribution

It offers a tighter performance guarantee analysis of the setcover greedy algorithm and establishes a new lower bound, comparing its worst-case performance to the information content heuristic.

Findings

Performance guarantee improved to 1.1354 ln n

Lower bound of 1.0004609 ln n established

Information content heuristic slightly better in worst case

Abstract

Setcover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of performance guarantee of this algorithm. The author improves the performance guarantee $2\ln n$ which derives from set cover problem to $1.1354\ln n$ by applying the potential function technique. In addition, the author gives a nontrivial lower bound $1.0004609\ln n$ of performance guarantee of this algorithm. This lower bound, together with the matching bound of information content heuristic, confirms the fact information content heuristic is slightly better than setcover greedy algorithm in worst case.