Chaining Multiple - Alignment Fragments in Sub - Quadratic

We describe a multiple-sequence alignment algorithm for determining the highest-scoring alignment that can be obtained by chaining together non-overlapping subalignments selected from a given collection of such \fragments". For a given set of K sequences, a problem instance consists of a set of F precomputed fragments, an alignment score for each fragment, and a \gap" penalty function that assigns a cost for chaining two fragments together. When interpreted as a maximum weight path problem in a directed acyclic graph, it is computable in (F 2) time. Here we instead interpret the problem as \K-dimensional sparse dynamic programming" and take advantage of its underlying geometric nature. Assuming K < log F, our algorithm runs in time O(F log K F) and space O(KF log K?1 F), making it the rst sub-quadratic sparse dynamic programming algorithm for the case K > 2.