Algorithms for local alignment with length constraints

The local sequence alignment problem is the detection of similar subsequences in two given sequences of lengths n greater than or equal to 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 Delta of the optimum score for any given positive integer Delta. The algorithm runs in time O(nmT/Delta) using O(mT/Delta) 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.