Optimal Deterministic Group Testing Algorithms to Estimate the Number of Defectives

Nader H. Bshouty, Catherine A. Haddad-Zaknoon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the problem of estimating the number of defective items d within a pile of n elements up to a multiplicative factor of Δ> 1, using deterministic group testing algorithms. We bring lower and upper bounds on the number of tests required in both the adaptive and the non-adaptive deterministic settings given an upper bound D on the defectives number. For the adaptive deterministic settings, our results show that, any algorithm for estimating the defectives number up to a multiplicative factor of Δ must make at least Ω((D/ Δ2) log (n/ D) ) tests. This extends the same lower bound achieved in [1] for non-adaptive algorithms. Moreover, we give a polynomial time adaptive algorithm that shows that our bound is tight up to a small additive term. For non-adaptive algorithms, an upper bound of O((D/ Δ2) (log (n/ D) + log Δ) ) is achieved by means of non-constructive proof. This improves the lower bound Ω((log D) / (log Δ) ) Dlog n) from [1] and matches the lower bound up to a small additive term. In addition, we study polynomial time constructive algorithms. We use existing polynomial time constructible expander regular bipartite graphs, extractors and condensers to construct two polynomial time algorithms. The first algorithm makes O((D1+o(1)/ Δ2) · log n) tests, and the second makes (D/ Δ2) · Quazipoly (log n) tests. This is the first explicit construction with an almost optimal test complexity.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 14th International Conference, COCOA 2020, Proceedings
EditorsWeili Wu, Zhongnan Zhang
PublisherSpringer Science and Business Media Deutschland GmbH
Pages393-410
Number of pages18
ISBN (Print)9783030648428
DOIs
StatePublished - 2020
Event14th International Conference on Combinatorial Optimization and Applications, COCOA 2020 - Dallas, United States
Duration: 11 Dec 202013 Dec 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12577 LNCS

Conference

Conference14th International Conference on Combinatorial Optimization and Applications, COCOA 2020
Country/TerritoryUnited States
CityDallas
Period11/12/2013/12/20

Keywords

  • Deterministic group testing
  • Group testing
  • Pooling design

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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