A Scalable Approximation Algorithm for Weighted Longest Common Subsequence

This work introduces novel parallel methods for weighted longest common subsequence (WLCS) and its generalization, allsubstrings WLCS. Previous work developed efficient algorithms for these problems via Monge matrix multiplication, which is a limiting factor for further improvement. Diverging from these approaches, we relax the algorithm's optimality guarantee in a controlled way, using a different, natural dynamic program which can be sketched and solved in a divideand-conquer manner that is efficient to parallelize. Additionally, to compute the base case of our algorithm, we develop a novel and efficient method for all-substrings WLCS inspired by previous work on unweighted all-substrings LCS, exploiting the typically small range of weights. Our method fits in most parallel models of computation, including the PRAM and the BSP model. To the best of our knowledge this is the fastest (1 -epsilon)-approximation algorithm for all-substrings WLCS and WLCS in BSP. Further, this is the asymptotically fastest parallel algorithm for weighted LCS as the number of processors increases.