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Parallel Algorithm for Pattern Matching Problems Under Substring Consistent Equivalence Relations

Authors Davaajav Jargalsaikhan, Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

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ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • parallel algorithm
  • substring consistent equivalence relation
  • pattern matching

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Abstract

Given a text and a pattern over an alphabet, the pattern matching problem searches for all occurrences of the pattern in the text. An equivalence relation ≈ is a substring consistent equivalence relation (SCER), if for two strings X and Y, X ≈ Y implies |X| = |Y| and X[i:j] ≈ Y[i:j] for all 1 ≤ i ≤ j ≤ |X|. In this paper, we propose an efficient parallel algorithm for pattern matching under any SCER using the "duel-and-sweep" paradigm. For a pattern of length m and a text of length n, our algorithm runs in O(ξ_m^t log³ m) time and O(ξ_m^w ⋅ n log² m) work, with O(τ_n^t + ξ_m^t log² m) time and O(τ_n^w + ξ_m^w ⋅ m log² m) work preprocessing on the Priority Concurrent Read Concurrent Write Parallel Random-Access Machines (P-CRCW PRAM), where τ_n^t, τ_n^w, ξ_m^t, and ξ_m^w are parameters dependent on SCERs, which are often linear in n and m, respectively.

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Davaajav Jargalsaikhan, Diptarama Hendrian, Ryo Yoshinaka, and Ayumi Shinohara. Parallel Algorithm for Pattern Matching Problems Under Substring Consistent Equivalence Relations. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CPM.2022.28

Author Details

Davaajav Jargalsaikhan
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Diptarama Hendrian
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Ryo Yoshinaka
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Ayumi Shinohara
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

Funding

  • Hendrian, Diptarama: JSPS KAKENHI Grant Number JP19K20208
  • Yoshinaka, Ryo: JSPS KAKENHI Grant Numbers JP18K11150 and JP20H05703
  • Shinohara, Ayumi: JSPS KAKENHI Grant Number JP21K11745

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