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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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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.

Cite AsGet BibTex

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

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.

Subject Classification

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

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