Bounds for Resquencing by Hybridization

We study the problem of finding the sequence of an unknown DNA fragment given the set of its k-long subsequences and a homologous sequence, namely a sequence that is similar to the target sequence. Such a sequence is available in some applications, e.g., when detecting single nucleotide polymorphisms. Pe’er and Shamir studied this problem and presented a heuristic algorithm for it. In this paper, we give an algorithm with provable performance: We show that under some assumptions, the algorithm can reconstruct a random sequence of length O(4 k ) with high probability. We also show that no algorithm can reconstruct sequences of length Ω(logk·4 k ).

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