Algorithms for local alignment with length constraints

Abstract

The local sequence alignment problem is the detection of similar subsequences in two given sequences of lengths n ≥ m. Unfortunately the common notion of local alignment suffers from some well known anomalies which result from not taking into account the lengths of the aligned subsequences. We introduce the length restricted local alignment problem which includes as a constraint an upper limit T on the length of one of the subsequences to be aligned. We propose an efficient approximation algorithm, which finds a solution satisfying the length bound, and whose score is within difference Δ of the optimum score for any given positive integer Δ. The algorithm runs in time O(nmT/Δ) using O(mT/Δ) space. We also introduce the cyclic local alignment problem and show how our idea can be applied to this case as well. This is a dual approach to the well-known cyclic edit distance problem.