Dynamic Programming Based Approximation Algorithms for Sequence Alignment with Constraints

Pairwise local alignment is one of the most important problems in sequence analysis in computational biology. Classical dynamic programming solution to this problem searches for two segments with maximum similarity score by discarding poorly conserved initial and terminal fragments. As a consequence, an alignment returned as optimal may contain a mosaic of well-conserved fragments arti cially connected by poorly-conserved or even unrelated fragments. In an attempt to solve the problems associated with the classical de nition of local similarity, several approaches have rede ned the objective of local alignment to incorporate segment lengths. These approaches give rise to problems with varying objective functions and constraints. When direct dynamic programming solutions exist for the constrained versions, the time complexity of the resulting exact algorithm is prohibitive. We present a survey of approximation algorithms and complexity results for each of these problems.