Parallel algorithm for pattern matching problems under substring consistent equivalence relations
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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,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^tlog^3 m) time and O(ξ_m^w· n log^2 m) work, with O(τ_n^t + ξ_m^tlog^2 m) time and O(τ_n^w + ξ_m^w· m log^2 m) work preprocessing on the Priority Concurrent Read Concurrent Write Parallel Random-Access Machines (P-CRCW PRAM).
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