# On the optimality of some group testing algorithms

## TL;DR

This paper analyzes the optimality of group testing algorithms, showing that the DD algorithm is suboptimal for certain parameters and that SCOMP and LP-based algorithms are at least as effective for large defect rates.

## Contribution

The paper provides new bounds on the rate of the DD algorithm and establishes the optimality of SCOMP and LP-based algorithms for specific defect proportions.

## Key findings

- DD is suboptimal for .41 < heta < 0.5
- SCOMP and LP algorithms achieve at least the same rate as DD for heta .5
- New upper bounds on the rate of the DD algorithm are derived.

## Abstract

We consider Bernoulli nonadaptive group testing with $k = \Theta(n^\theta)$ defectives, for $\theta \in (0,1)$. The practical definite defectives (DD) detection algorithm is known to be optimal for $\theta \geq 1/2$. We give a new upper bound on the rate of DD, showing that DD is strictly suboptimal for $\theta < 0.41$. We also show that the SCOMP algorithm and algorithms based on linear programming achieve a rate at least as high as DD, so in particular are also optimal for $\theta \geq 1/2$.