Bounds for Parametric Sequence Comparison
نویسندگان
چکیده
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 3(n=2 )+O(n log n) bound on the worst-case number of distinct optimum alignments for two sequences of length n as the parameters are varied. This re7nes a O(n) upper bound by Gus7eld et al., answering a question posed by Pevzner and Waterman. Our lower bound requires an unbounded alphabet. For strings over a binary alphabet, we prove a (n) lower bound. For the parametric global alignment of k¿ 2 sequences under sum-of-pairs scoring we prove a 3(( k2 )n=2 ) 2=3 + O(kn log n) upper bound on the number of distinct optimality regions and a (n) lower bound, partially answering a problem of Pevzner. Based on experimental evidence, we conjecture that for two random sequences, the number of optimality regions is approximately √ n with high probability. ? 2002 Elsevier Science B.V. All rights reserved.
منابع مشابه
Some properties of the parametric relative operator entropy
The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...
متن کاملLower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces
Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...
متن کاملSome inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...
متن کاملOn Moments of the Concomitants of Classic Record Values and Nonparametric Upper Bounds for the Mean under the Farlie-Gumbel-Morgenstern Model
In a sequence of random variables, record values are observations that exceed or fall below the current extreme value.Now consider a sequence of pairwise random variables {(Xi,Yi), i>=1}, when the experimenter is interested in studying just thesequence of records of the first component, the second component associated with a record value of the first one is termed the concomitant of that ...
متن کاملMore inequalities for Laplacian indices by way of majorization
The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...
متن کامل