Fast and Cache-Oblivious Dynamic Programming with Local Dependencies

Abstract

String comparison such as sequence alignment, edit distance computation, longest common subsequence computation, and approximate string matching is a key task (and often computational bottleneck) in large-scale textual information retrieval. For instance, algorithms for sequence alignment are widely used in bioinformatics to compare DNA and protein sequences. These problems can all be solved using essentially the same dynamic programming scheme over a two-dimensional matrix, where each entry depends locally on at most 3 neighboring entries. We present a simple, fast, and cache-oblivious algorithm for this type of local dynamic programming suitable for comparing large-scale strings. Our algorithm outperforms the previous state-of-the-art solutions. Surprisingly, our new simple algorithm is competitive with a complicated, optimized, and tuned implementation of the best cache-aware algorithm. Additionally, our new algorithm generalizes the best known theoretical complexity trade-offs for the problem.