Abstract
For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p| + r · log n + o · log2 n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.
| Original language | English |
|---|---|
| Title of host publication | 30th International Symposium on Algorithms and Computation, ISAAC 2019 |
| Editors | Pinyan Lu, Guochuan Zhang |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959771306 |
| DOIs | |
| Publication status | Published - Dec 2019 |
| Event | 30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China Duration: Dec 8 2019 → Dec 11 2019 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 149 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 30th International Symposium on Algorithms and Computation, ISAAC 2019 |
|---|---|
| Country | China |
| City | Shanghai |
| Period | 12/8/19 → 12/11/19 |
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All Science Journal Classification (ASJC) codes
- Software
Cite this
An improved data structure for left-right maximal generic words problem. / Fujishige, Yuta; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.
30th International Symposium on Algorithms and Computation, ISAAC 2019. ed. / Pinyan Lu; Guochuan Zhang. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 40 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 149).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - An improved data structure for left-right maximal generic words problem
AU - Fujishige, Yuta
AU - Nakashima, Yuto
AU - Inenaga, Shunsuke
AU - Bannai, Hideo
AU - Takeda, Masayuki
PY - 2019/12
Y1 - 2019/12
N2 - For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p| + r · log n + o · log2 n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.
AB - For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p| + r · log n + o · log2 n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.
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UR - http://www.scopus.com/inward/citedby.url?scp=85076353657&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2019.40
DO - 10.4230/LIPIcs.ISAAC.2019.40
M3 - Conference contribution
AN - SCOPUS:85076353657
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 30th International Symposium on Algorithms and Computation, ISAAC 2019
A2 - Lu, Pinyan
A2 - Zhang, Guochuan
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ER -