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On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching

Authors Johannes Fischer, Dominik Köppl, Florian Kurpicz

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Johannes Fischer
Dominik Köppl
Florian Kurpicz

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Johannes Fischer, Dominik Köppl, and Florian Kurpicz. On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 26:1-26:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CPM.2016.26

Abstract

We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with p processors. Given a static text of length n, we first show how to compute the suffix array interval of a given pattern of length m in O(m/p + lg p + lg lg p * lg lg n) time for p <= m. For approximate pattern matching with k differences or mismatches, we show how to compute all occurrences of a given pattern in O((m^k sigma^k)/p max (k, lg lg n) + (1+m/p) lg p * lg lg n + occ} time, where sigma is the size of the alphabet and p <= sigma^k m^k. The workhorse of our algorithms is a data structure for merging suffix array intervals quickly: Given the suffix array intervals for two patterns P and P', we present a data structure for computing the interval of PP' in O(lg lg n) sequential time, or in O(1 + lg_p lg n) parallel time. All our data structures are of size O(n) bits (in addition to the suffix array).

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Keywords
  • parallel algorithms
  • pattern matching
  • approximate string matching

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