TY - GEN

T1 - Computing convolution on grammar-compressed text

AU - Tanaka, Toshiya

AU - Tomohiro, I.

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - The convolution between a text string S of length N and a pattern string P of length m can be computed in Ο(N logm) time by FFT. It is known that various types of approximate string matching problems are reducible to convolution. In this paper, we assume that the input text string is given in a compressed form, as a straight-line program (SLP), which is a context free grammar in the Chomsky normal form that derives a single string. Given an SLP S of size n describing a text S of length N, and an uncompressed pattern P of length m, we present a simple Ο(nmlogm)-time algorithm to compute the convolution between S and P. We then show that this can be improved to Ο(min{nm,N - α} logm) time, where α ≥ 0 is a value that represents the amount of redundancy that the SLP captures with respect to the length-m substrings. The key of the improvement is our new algorithm that computes the convolution between a trie of size r and a pattern string P of length m in Ο(r logm) time.

AB - The convolution between a text string S of length N and a pattern string P of length m can be computed in Ο(N logm) time by FFT. It is known that various types of approximate string matching problems are reducible to convolution. In this paper, we assume that the input text string is given in a compressed form, as a straight-line program (SLP), which is a context free grammar in the Chomsky normal form that derives a single string. Given an SLP S of size n describing a text S of length N, and an uncompressed pattern P of length m, we present a simple Ο(nmlogm)-time algorithm to compute the convolution between S and P. We then show that this can be improved to Ο(min{nm,N - α} logm) time, where α ≥ 0 is a value that represents the amount of redundancy that the SLP captures with respect to the length-m substrings. The key of the improvement is our new algorithm that computes the convolution between a trie of size r and a pattern string P of length m in Ο(r logm) time.

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U2 - 10.1109/DCC.2013.53

DO - 10.1109/DCC.2013.53

M3 - Conference contribution

AN - SCOPUS:84881048177

SN - 9780769549651

T3 - Data Compression Conference Proceedings

SP - 451

EP - 460

BT - Proceedings - DCC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2013 Data Compression Conference, DCC 2013

Y2 - 20 March 2013 through 22 March 2013

ER -