Group testing in graphs

Justie Su-tzu Juan () and Gerard J. Chang ()
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Justie Su-tzu Juan: National Chi Nan University, Puli
Gerard J. Chang: National Taiwan University

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 2, 113-119

Abstract: Abstract This paper studies the group testing problem in graphs as follows. Given a graph G=(V,E), determine the minimum number t(G) such that t(G) tests are sufficient to identify an unknown edge e with each test specifies a subset X⊆V and answers whether the unknown edge e is in G[X] or not. Damaschke proved that ⌈log 2 e(G)⌉≤t(G)≤⌈log 2 e(G)⌉+1 for any graph G, where e(G) is the number of edges of G. While there are infinitely many complete graphs that attain the upper bound, it was conjectured by Chang and Hwang that the lower bound is attained by all bipartite graphs. Later, they proved that the conjecture is true for complete bipartite graphs. Chang and Juan verified the conjecture for bipartite graphs G with e(G)≤24 or $2^{k-1}

Keywords: Group testing; Graph; Bipartite graph; Sample space; Algorithm (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-007-9068-2

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