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DAWGs for Parameterized Matching: Online Construction and Related Indexing Structures

Authors Katsuhito Nakashima, Noriki Fujisato, Diptarama Hendrian , Yuto Nakashima , Ryo Yoshinaka , Shunsuke Inenaga , Hideo Bannai , Ayumi Shinohara , Masayuki Takeda

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ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • parameterized matching
  • suffix trees
  • DAWGs
  • suffix automata

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Abstract

Two strings x and y over Σ ∪ Π of equal length are said to parameterized match (p-match) if there is a renaming bijection f:Σ ∪ Π → Σ ∪ Π that is identity on Σ and transforms x to y (or vice versa). The p-matching problem is to look for substrings in a text that p-match a given pattern. In this paper, we propose parameterized suffix automata (p-suffix automata) and parameterized directed acyclic word graphs (PDAWGs) which are the p-matching versions of suffix automata and DAWGs. While suffix automata and DAWGs are equivalent for standard strings, we show that p-suffix automata can have Θ(n²) nodes and edges but PDAWGs have only O(n) nodes and edges, where n is the length of an input string. We also give O(n |Π| log (|Π| + |Σ|))-time O(n)-space algorithm that builds the PDAWG in a left-to-right online manner. As a byproduct, it is shown that the parameterized suffix tree for the reversed string can also be built in the same time and space, in a right-to-left online manner.

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Katsuhito Nakashima, Noriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, Hideo Bannai, Ayumi Shinohara, and Masayuki Takeda. DAWGs for Parameterized Matching: Online Construction and Related Indexing Structures. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CPM.2020.26

Author Details

Katsuhito Nakashima
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Noriki Fujisato
  • Department of Informatics, Kyushu University, Fukuoka, Japan
Diptarama Hendrian
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Yuto Nakashima
  • Department of Informatics, Kyushu University, Fukuoka, Japan
Ryo Yoshinaka
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Shunsuke Inenaga
  • Department of Informatics, Kyushu University, Fukuoka, Japan
  • PRESTO, Japan Science and Technology Agency, Kawaguchi, Japan
Hideo Bannai
  • M&D Data Science Center, Tokyo Medical and Dental University, Tokyo, Japan
Ayumi Shinohara
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Masayuki Takeda
  • Department of Informatics, Kyushu University, Fukuoka, Japan

Funding

  • Hendrian, Diptarama: JSPS KAKENHI Grant Number JP19K20208.
  • Nakashima, Yuto: JSPS KAKENHI Grant Number JP18K18002.
  • Yoshinaka, Ryo: JSPS KAKENHI Grant Number JP18H04091.
  • Inenaga, Shunsuke: JSPS KAKENHI Grant Number JP17H01697, JST PRESTO Grant Number JPMJPR1922.
  • Bannai, Hideo: JSPS KAKENHI Grant Numbers JP16H02783, JP20H04141.
  • Shinohara, Ayumi: JSPS KAKENHI Grant Number JP15H05706.
  • Takeda, Masayuki: JSPS KAKENHI Grant Number JP18H04098.

References

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