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Computing Runs on a Trie

Authors Ryo Sugahara, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai , Masayuki Takeda

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Author Details

Ryo Sugahara
  • Department of Informatics, Kyushu University, Japan
Yuto Nakashima
  • Department of Informatics, Kyushu University, Japan
Shunsuke Inenaga
  • Department of Informatics, Kyushu University, Japan
Hideo Bannai
  • Department of Informatics, Kyushu University, Japan
Masayuki Takeda
  • Department of Informatics, Kyushu University, Japan

Funding

  • Nakashima, Yuto: Supported by JSPS KAKENHI Grant Number JP18K18002.
  • Inenaga, Shunsuke: Supported by JSPS KAKENHI Grant Number JP17H01697.
  • Bannai, Hideo: Supported by JSPS KAKENHI Grant Number JP16H02783.
  • Takeda, Masayuki: Supported by JSPS KAKENHI Grant Number JP18H04098.

Cite As Get BibTex

Ryo Sugahara, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Computing Runs on a Trie. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 23:1-23:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CPM.2019.23

Abstract

A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a rooted edge-labeled tree where the endpoints of the path must be a descendant/ancestor of the other. For a trie with n edges, we show that the number of runs is less than n. We also show an O(n sqrt{log n}log log n) time and O(n) space algorithm for counting and finding the shallower endpoint of all runs. We further show an O(n log n) time and O(n) space algorithm for finding both endpoints of all runs. We also discuss how to improve the running time even more.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Combinatorics on words
Keywords
  • runs
  • Lyndon words

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References

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