Graph-constrained group testing

Mahdi Cheraghchi, Amin Karbasi, Soheil Mohajer, Venkatesh Saligrama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

Non-adaptive group testing involves grouping arbitrary subsets of n items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagation we formulate non-adaptive group testing problems on graphs. Unlike conventional group testing problems each group here must conform to the constraints imposed by a graph. For instance, items can be associated with vertices and each pool is any set of nodes that must be path connected. In this paper we associate a test with a random walk. In this context conventional group testing corresponds to the special case of a complete graph on n vertices. For interesting classes of graphs we arrive at a rather surprising result, namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed. Specifically, if T(n) corresponds to the mixing time of the graph G, we show that with m = O(d 2T2(n) log(n/d)) non-adaptive tests, one can identify the defective items. Consequently, for the Erdos-Rényi random graph G(n, p), as well as expander graphs with constant spectral gap, it follows that m = O(d2 log3 n) non-adaptive tests are sufficient to identify d defective items. We next consider a specific scenario that arises in network tomography and show that m = O(d3 log3 n) non-adaptive tests are sufficient to identify d defective items. We also consider noisy counterparts of the graph constrained group testing problem and develop parallel results for these cases.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages1913-1917
Number of pages5
DOIs
StatePublished - 2010
Event2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States
Duration: Jun 13 2010Jun 18 2010

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8103

Other

Other2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/TerritoryUnited States
CityAustin, TX
Period6/13/106/18/10

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