DeepAI AI Chat
Log In Sign Up

Group Testing for Efficiently Sampling Hypergraphs When Tests Have Variable Costs

by   Laurence A. Clarfeld, et al.

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.


Generalized Non-adaptive Group Testing

In the problem of classical group testing one aims to identify a small s...

A Diagonal Splitting Algorithm for Adaptive Group Testing

Group testing enables to identify infected individuals in a population u...

The Stochastic Score Classification Problem

Consider the following Stochastic Score Classification Problem. A doctor...

A Computational Model for Logical Analysis of Data

Initially introduced by Peter Hammer, Logical Analysis of Data is a meth...

A new life of Pearson's skewness

In this work we show how coupling and stochastic dominance methods can b...

Improved algorithms for non-adaptive group testing with consecutive positives

The goal of group testing is to efficiently identify a few specific item...

Critical Limits in a Bump Attractor Network of Spiking Neurons

A bump attractor network is a model that implements a competitive neuron...