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

N1 - Funding Information:
Funding Yuto Nakashima: Supported by JSPS KAKENHI Grant Number JP18K18002. Shunsuke Inenaga: Supported by JSPS KAKENHI Grant Number JP17H01697. Hideo Bannai: Supported by JSPS KAKENHI Grant Number JP16H02783. Masayuki Takeda: Supported by JSPS KAKENHI Grant Number JP18H04098.

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.

UR - http://www.scopus.com/inward/record.url?scp=85076353657&partnerID=8YFLogxK

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

T2 - 30th International Symposium on Algorithms and Computation, ISAAC 2019

Y2 - 8 December 2019 through 11 December 2019

ER -