Abstract
Exact string matching is a problem that computer programmers face on a regular basis, and full-text indexes like the suffix tree or the suffix array provide fast string search over large texts. In the last decade, research on compressed indexes has flourished because the main problem in large-scale applications is the space consumption of the index. Nowadays, the most successful compressed indexes are able to obtain almost optimal space and search time simultaneously. It is known that a myriad of sequence analysis and comparison problems can be solved efficiently with established data structures like the suffix tree or the suffix array, but algorithms on compressed indexes that solve these problem are still lacking at present. Here, we show that matching statistics and maximal exact matches between two strings S 1 and S 2 can be computed efficiently by matching S 2 backwards against a compressed index of S 1.
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References
Weiner, P.: Linear pattern matching algorithms. Proc. 14th IEEE Annual Symposium on Switching and Automata Theory. 1–11 (1973)
Apostolico, A.: The myriad virtues of subword trees. In: Combinatorial Algorithms on Words, pp. 85–96. Springer, Heidelberg (1985)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Cambridge University Press, New York (1997)
Manber, U., Myers, E.: Suffix arrays: A new method for on-line string searches. SIAM Journal on Computing 22(5), 935–948 (1993)
Ferragina, P., Manzini, G.: Opportunistic data structures with applications. In: Proc. IEEE Symposium on Foundations of Computer Science, pp. 390–398 (2000)
Burrows, M., Wheeler, D.: A block-sorting lossless data compression algorithm. Research Report 124, Digital Systems Research Center (1994)
Chang, W., Lawler, E.: Sublinear approximate string matching and biological applications. Algorithmica 12(4/5), 327–344 (1994)
Teo, C., Vishwanathan, S.: Fast and space efficient string kernels using suffix arrays. In: Proc. 23rd Conference on Machine Learning, pp. 929–936. ACM Press, New York (2003)
Rahmann, S.: Fast and sensitive probe selection for DNA chips using jumps in matching statistics. In: Proc. 2nd IEEE Computer Society Bioinformatics Conference, pp. 57–64 (2003)
Kurtz, S., Phillippy, A., Delcher, A., Smoot, M., Shumway, M., Antonescu, C., Salzberg, S.: Versatile and open software for comparing large genomes. Genome Biology 5, R12 (2004)
Abouelhoda, M., Kurtz, S., Ohlebusch, E.: CoCoNUT: An efficient system for the comparison and analysis of genomes. BMC Bioinformatics 9, 476 (2008)
Puglisi, S., Smyth, W., Turpin, A.: A taxonomy of suffix array construction algorithms. ACM Computing Surveys 39(2), 1–31 (2007)
Grossi, R., Gupta, A., Vitter, J.: High-order entropy-compressed text indexes. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms, pp. 841–850 (2003)
Navarro, G., Mäkinen, V.: Compressed full-text indexes. ACM Computing Surveys 39(1), Article 2 (2007)
Kasai, T., Lee, G., Arimura, H., Arikawa, S., Park, K.: Linear-time longest-common-prefix computation in suffix arrays and its applications. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 181–192. Springer, Heidelberg (2001)
Sadakane, K.: Compressed suffix trees with full functionality. Theory of Computing Systems 41, 589–607 (2007)
Abouelhoda, M., Kurtz, S., Ohlebusch, E.: Replacing suffix trees with enhanced suffix arrays. Journal of Discrete Algorithms 2, 53–86 (2004)
Ohlebusch, E., Gog, S.: A compressed enhanced suffix array supporting fast string matching. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds.) SPIRE 2009. LNCS, vol. 5721, pp. 51–62. Springer, Heidelberg (2009)
Fischer, J., Mäkinen, V., Navarro, G.: Faster entropy-bounded compressed suffix trees. Theoretical Computer Science 410(51), 5354–5364 (2009)
Russo, L., Navarro, G., Oliveira, A.: Parallel and distributed compressed indexes. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 348–360. Springer, Heidelberg (2010)
Khan, Z., Bloom, J., Kruglyak, L., Singh, M.: A practical algorithm for finding maximal exact matches in large sequence data sets using sparse suffix arrays. Bioinformatics 25, 1609–1616 (2009)
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Ohlebusch, E., Gog, S., Kügel, A. (2010). Computing Matching Statistics and Maximal Exact Matches on Compressed Full-Text Indexes. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_36
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DOI: https://doi.org/10.1007/978-3-642-16321-0_36
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