A linear algorithm for string reconstruction in the reverse complement equivalence model

Authors:
Ferdinando Cicalese;Péter L. Erds;Zsuzsanna Lipták
Affiliations:
Dipartimento di Informatica ed Applicazioni, University of Salerno, Italy;A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O. Box 127, H-1364, Hungary;AG Genominformatik, Technische Fakultät, Bielefeld University, Germany
Venue:
Journal of Discrete Algorithms
Year:
2012

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Abstract

In the reverse complement equivalence model, it is not possible to distinguish a string from its reverse complement. We show that one can still reconstruct a string of length n, up to reverse complement, using a linear number of subsequence queries of bounded length. We first give the proof for strings over a binary alphabet, and then extend it to arbitrary finite alphabets. A simple information theoretic lower bound proves the number of queries to be asymptotically tight. Furthermore, our result is optimal w.r.t. the bound on the query length given in Erdos et al. (2006) [6].