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.
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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 -