Group Testing for Efficiently Sampling Hypergraphs When Tests Have Variable Costs

TL;DR

This paper compares deterministic and stochastic group testing algorithms for hypergraph edge detection with variable test costs, revealing trade-offs in total tests versus positive tests based on cost ratios.

Contribution

It introduces a tunable problem setup to evaluate and compare the efficiency of deterministic and stochastic group testing algorithms in hypergraphs with variable test costs.

Findings

Deterministic splitting uses fewer total tests.

Stochastic splitting results in fewer positive tests.

Optimal initial group size depends on defect prevalence and cost ratio.

Abstract

In the group-testing literature, efficient algorithms have been developed to minimize the number of tests required to identify all minimal "defective" sub-groups embedded within a larger group, using deterministic group splitting with a generalized binary search. In a separate literature, researchers have used a stochastic group splitting approach to efficiently sample from the intractable number of minimal defective sets of outages in electrical power systems that trigger large cascading failures, a problem in which positive tests can be much more computationally costly than negative tests. In this work, we generate test problems with variable numbers of defective sets and a tunable positive:negative test cost ratio to compare the efficiency of deterministic and stochastic adaptive group splitting algorithms for identifying defective edges in hypergraphs. For both algorithms, we show that the optimal initial group size is a function of both the prevalence of defective sets and the positive:negative test cost ratio. We find that deterministic splitting requires fewer total tests but stochastic splitting requires fewer positive tests, such that the relative efficiency of these two approaches depends on the positive:negative test cost ratio. We discuss some real-world applications where each of these algorithms is expected to outperform the other.