TY - JOUR

T1 - Efficiently computing runs on a trie

AU - Sugahara, Ryo

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP18K18002 (YN), JP17H01697 (SI), JP20H04141 (HB), JP18H04098 (MT), JST ACT-X Grant Number JPMJAX200K (YN), and JST PRESTO Grant Number JPMJPR1922 (SI).
Publisher Copyright:
© 2021 The Authors

PY - 2021/10/2

Y1 - 2021/10/2

N2 - 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 each edge is labeled with a single symbol, and 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 asymptotic lower bound on the maximum density of runs in tries: limn→∞ρT(n)/n>0.9932348 where ρT(n) is the maximum number of runs in a trie with n edges. Furthermore, we also show an O(nloglogn) time and O(n) space algorithm for finding all runs.

AB - 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 each edge is labeled with a single symbol, and 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 asymptotic lower bound on the maximum density of runs in tries: limn→∞ρT(n)/n>0.9932348 where ρT(n) is the maximum number of runs in a trie with n edges. Furthermore, we also show an O(nloglogn) time and O(n) space algorithm for finding all runs.

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U2 - 10.1016/j.tcs.2021.07.011

DO - 10.1016/j.tcs.2021.07.011

M3 - Article

AN - SCOPUS:85111058949

VL - 887

SP - 143

EP - 151

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -