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√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.
| Original language | English |
|---|---|
| Title of host publication | 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 |
| Editors | Nadia Pisanti, Solon P. Pissis |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959771030 |
| DOIs | |
| Publication status | Published - Jun 1 2019 |
| Event | 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 - Pisa, Italy Duration: Jun 18 2019 → Jun 20 2019 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 128 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 |
|---|---|
| Country | Italy |
| City | Pisa |
| Period | 6/18/19 → 6/20/19 |
All Science Journal Classification (ASJC) codes
- Software
Cite this
Computing runs on a trie. / Sugahara, Ryo; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.
30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019. ed. / Nadia Pisanti; Solon P. Pissis. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 23 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 128).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Computing runs on a trie
AU - Sugahara, Ryo
AU - Nakashima, Yuto
AU - Inenaga, Shunsuke
AU - Bannai, Hideo
AU - Takeda, Masayuki
PY - 2019/6/1
Y1 - 2019/6/1
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 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√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.
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 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√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.
UR - http://www.scopus.com/inward/record.url?scp=85068064626&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85068064626&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CPM.2019.23
DO - 10.4230/LIPIcs.CPM.2019.23
M3 - Conference contribution
AN - SCOPUS:85068064626
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019
A2 - Pisanti, Nadia
A2 - Pissis, Solon P.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ER -