Fast and Cache-Oblivious Dynamic Programming with Local Dependencies
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.
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- 2.Bille, P.: Faster approximate string matching for short patterns. Theory Comput. Syst. (2011) (to appear)Google Scholar
- 4.Chowdhury, R.A., Ramachandran, V.: Cache-oblivious dynamic programming. In: Proc. 17th Symp. on Discrete Algorithms, pp. 591–600 (2006)Google Scholar
- 5.Chowdhury, R.A., Ramachandran, V.: Cache-efficient dynamic programming algorithms for multicores. In: Proc. 20th Symp. on Parallelism in Algorithms and Architectures, pp. 207–216 (2008), http://doi.acm.org/10.1145/1378533.1378574
- 9.Driga, A., Lu, P., Schaeffer, J., Szafron, D., Charter, K., Parsons, I.: FastLSA: A fast, linear-space, parallel and sequential algorithm for sequence alignment. In: Proc. Intl. Conf. on Parallel Processing, pp. 48–57 (2005)Google Scholar
- 11.Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. In: Proc. 40th Symp. Foundations of Computer Science, pp. 285–297 (1999)Google Scholar
- 12.Gusfield, D.: Algorithms on strings, trees, and sequences: computer science and computational biology, Cambridge (1997)Google Scholar
- 13.Hermelin, D., Landau, G.M., Landau, S., Weimann, O.: A unified algorithm for accelerating edit-distance computation via text-compression. In: Proc. 26th Symp. Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), vol. 3, pp. 529–540 (2009)Google Scholar
- 18.Myers, E.W., Miller, W.: Optimal alignments in linear space. Comput. Appl. Biosci. 4(1), 11–17 (1988)Google Scholar