Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Bounds for parametric sequence comparison
Discrete Applied Mathematics
Algebraic Statistics for Computational Biology
Algebraic Statistics for Computational Biology
Hi-index | 0.04 |
In parametric sequence alignment, optimal alignments of two sequences are computed as a function of matches, mismatches and spaces, producing many different optimal alignments. In the two-parameter case, Gusfield et al shows that the number of distinct optimal alignment summaries for a pair of sequences is O(n^2^/^3). Here we construct binary sequences of length n with 3/(2^7^/^3@p^2^/^3)n^2^/^3+O(n^1^/^3logn) distinct optimal alignment summaries. This shows that the upper bound given by Gusfield et al. is tight over all alphabets, thereby disproving the ''n conjecture''. Thus the maximum number of distinct optimal alignment summaries over all pairs of length n sequences is @Q(n^2^/^3).