Sparse Dynamic Programming for Longest Common Subsequence from Fragments

Sparse Dynamic Programming has emerged as an essential tool for the design of efficient algorithms for optimization problems coming from such diverse areas as Computer Science, Computational Biology and Speech Recognition. We provide a new Sparse Dynamic Programming technique that extends the Hunt-Seymanski paradigm for the computation of the Longest Common Subsequence (LCS) and apply it to solve the LCS from Fragments problem: given a pair of strings X and Y (of length n and m, resp.) and a set M of matching substrings of X and Y, find the longest common subsequence based only on the symbol correspondences induced by the substrings.