Approximation to the mean curve in the LCS problem |
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Authors: | Clement Durringer Raphael Hauser Heinrich Matzinger |
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Affiliation: | 1. Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118, Route de Narbonne, 31062 Toulouse Cedex 4, France;2. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom;3. Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany |
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Abstract: | The problem of sequence comparison via optimal alignments occurs naturally in many areas of applications. The simplest such technique is based on evaluating a score given by the length of a longest common subsequence divided by the average length of the original sequences. In this paper we investigate the expected value of this score when the input sequences are random and their length tends to infinity. The corresponding limit exists but is not known precisely. We derive a theoretical large deviation, convex analysis and Monte Carlo based method to compute a consistent sequence of upper bounds on the unknown limit. An empirical practical version of our method produces promising numerical results. |
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Keywords: | primary, 05A16, 60F10, 65C05 secondary, 46N10, 92-08 |
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