Upper and Lower Bounds for Competitive Group Testing

TL;DR

This paper advances adaptive group testing by providing a more efficient algorithm with a competitive ratio below 1.452 and establishing a new lower bound of 1.31 for the competitive constant.

Contribution

It introduces a new algorithm with a competitive ratio under 1.452 and proves the first nontrivial lower bound of 1.31 for the competitive constant in adaptive group testing.

Findings

New algorithm with c < 1.452

First nontrivial lower bound c > 1.31

Improves upon previous algorithms from 2003

Abstract

We consider competitive algorithms for adaptive group testing problems. In the first part of the paper, we develop an algorithm with competitive constant c < 1.452 thus improving the up to now best known algorithms with constants 1.5+epsilon from 2003. In the second part, we prove the first nontrivial lower bound for competitive constants, namely that c is always larger than 1.31.