On a cyclic string-to-string correction problem
Information Processing Letters
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Dynamic Programming
Introduction to Algorithms
Journal of Computer and System Sciences - Computational biology 2002
Parametric Recomuting in Alignment Graphs
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
A Normalized Levenshtein Distance Metric
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Given two sequences X and Y, the classical dynamic programming solution to the local alignment problem searches for two subsequences I â聤聠 X and J â聤聠 Y with maximum similarity score under a given scoring scheme. In several applications, variants of this problem arise with different objectives and with length constraints on the subsequences I and J. This constraint can be explicit, such as requiring | I | + | J | â聣楼 t, or | J | â聣陇 T, or may be implicit such as in cyclic sequence comparison, or as in the maximization of length-normalized scores, and driven by practical considerations. We present a survey of approximation algorithms for various alignment problems with constraints, and several new approximation algorithms. These approximations are in two distinct senses: In one the constraints are satisfied but the score computed is within a prescribed tolerance of the optimum instead of the exact optimum. In another, the alignment returned is assured to have at least the optimum score with respect to the given constraints, but the length constraints are satisfied to within a prescribed tolerance from the required values. The algorithms proposed involve applications of techniques from fractional programming and dynamic programming.