Parametric Multiple Sequence Alignment and Phylogeny Construction
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
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We consider the problem of computing a global alignment between two or more sequences subject to varying mismatch and indel penalties. We prove a tight \mathbound on the worst-case number of distinct optimum alignments for two sequences of length n as the parameters are varied. This refines a \mathupper bound by Gusfield et al. Our lower bound requires an unbounded alphabet. For strings over a binary alphabet, we prove a \mathlower bound. For the parametric global alignment of \mathsequences under sum-of-pairs scoring we prove a \mathupper bound on the number of distinct optimality regions and a \mathlower bound. Based on experimental evidence, we conjecture that for two random sequences, the number of optimality regions is approximately \mathwith high probability.