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On the complexity and approximation of non-unique probe selection using d-disjunct matrix

Author

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  • My T. Thai

    (University of Florida)

  • Taieb Znati

    (University of Pittsburgh)

Abstract

In this paper, we studied the MINimum-d-Disjunct Submatrix (MIN-d-DS), which can be used to select the minimum number of non-unique probes for viruses identification. We prove that MIN-d-DS is NP-hard for any fixed d. Using d-disjunct matrix, we present an O(log k)-approximation algorithm where k is an upper bound on the maximum number of targets hybridized to a probe. We also present a (1+(d+1)log n)-approximation algorithm to identify at most d targets in the presence of experimental errors. Our approximation algorithms also yield a linear time complexity for the decoding algorithms.

Suggested Citation

  • My T. Thai & Taieb Znati, 2009. "On the complexity and approximation of non-unique probe selection using d-disjunct matrix," Journal of Combinatorial Optimization, Springer, vol. 17(1), pages 45-53, January.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:1:d:10.1007_s10878-008-9188-3
    DOI: 10.1007/s10878-008-9188-3
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    References listed on IDEAS

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    1. Hong Gao & F. K. Hwang & My T. Thai & Weili Wu & Taieb Znati, 2006. "Construction of d(H)-disjunct matrix for group testing in hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 297-301, November.
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