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Ternary Directed Acyclic Word Graphs

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Implementation and Application of Automata (CIAA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2759))

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Abstract

Given a set S of strings, a DFA accepting S offers a very time-efficient solution to the pattern matching problem over S. The key is how to implement such a DFA in the trade-off between time and space, and especially the choice of how to implement the transitions of each state is critical. Bentley and Sedgewick proposed an effective tree structure called ternary trees. The idea of ternary trees is to ‘implant’ the process of binary search for transitions into the structure of the trees themselves. This way the process of binary search becomes visible, and the implementation of the trees becomes quite easy. The directed acyclic word graph (DAWG) of a string w is the smallest DFA that accepts all suffixes of w, and requires only linear space. We apply the scheme of ternary trees to DAWGs, introducing a new data structure named ternary DAWGs (TDAWGs). We perform some experiments that show the efficiency of TDAWGs, compared to DAWGs in which transitions are implemented by tables and linked lists.

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Author information

Authors and Affiliations

  1. Department of Informatics, Kyushu University 33, Fukuoka, 812-8581, Japan

    Satoru Miyamoto, Shunsuke Inenaga, Masayuki Takeda & Ayumi Shinohara

  2. PRESTO, Japan Science and Technology Corporation (JST), Japan

    Shunsuke Inenaga, Masayuki Takeda & Ayumi Shinohara

Authors
  1. Satoru Miyamoto
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  2. Shunsuke Inenaga
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  3. Masayuki Takeda
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  4. Ayumi Shinohara
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, 99163, USA

    Zhe Dang

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© 2003 Springer-Verlag Berlin Heidelberg

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Miyamoto, S., Inenaga, S., Takeda, M., Shinohara, A. (2003). Ternary Directed Acyclic Word Graphs. In: Ibarra, O.H., Dang, Z. (eds) Implementation and Application of Automata. CIAA 2003. Lecture Notes in Computer Science, vol 2759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45089-0_12

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  • DOI: https://doi.org/10.1007/3-540-45089-0_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40561-0

  • Online ISBN: 978-3-540-45089-4

  • eBook Packages: Springer Book Archive

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