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A NOTE ON THE HU–HWANG–WANG CONJECTURE FOR GROUP TESTING

Part of: Combinatorics Graph theory Operations research and management science

Published online by Cambridge University Press:  01 April 2008

MING-GUANG LEU
MING-GUANG LEU*
Affiliation:
Department of Mathematics, National Central University, Chung-Li 32054, Taiwan (email: mleu@math.ncu.edu.tw)
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Abstract

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Hu et al. [“A boundary problem for group testing”, SIAM J. Algebraic Discrete Meth.2 (1981), 81–87] conjectured that the minimax test number to find d defectives in 3d items is 3d−1, a surprisingly difficult combinatorial problem about which very little is known. In this article we state three more conjectures and prove that they are all equivalent to the conjecture of Hu et al. Notably, as a byproduct, we also obtain an interesting upper bound for M(d,n).

Keywords

group testingalgorithm

MSC classification

Secondary: 05A15: Exact enumeration problems, generating functions 05C99: None of the above, but in this section 90B25: Reliability, availability, maintenance, inspection

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 561 - 571
Copyright
Copyright © Australian Mathematical Society 2008

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