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.
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The research of T. Znati was supported in part by National Science Foundation under grant CCF-0548895.
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Thai, M.T., Znati, T. On the complexity and approximation of non-unique probe selection using d-disjunct matrix. J Comb Optim 17, 45–53 (2009). https://doi.org/10.1007/s10878-008-9188-3
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DOI: https://doi.org/10.1007/s10878-008-9188-3