Name
Abstract | ||
|---|---|---|
The longest common extension (LCE) problem is to preprocess a given string w of length n so that the length of the longest common prefix between suffixes of w that start at any two given positions is answered quickly. In this paper, we present a data structure of O(z tau^2 + frac{n}{tau}) words of space which answers LCE queries in O(1) time and can be built in O(n log sigma) time, where 1 leq tau leq sqrt{n} is a parameter, z is the size of the Lempel-Ziv 77 factorization of w and sigma is the alphabet size. The proposed LCE data structure not access the input string w when answering queries, and thus w can be deleted after preprocessing. On top of this main result, we obtain further results using (variants of) our LCE data structure, which include the following:- For highly repetitive strings where the ztau^2 term is dominated by frac{n}{tau}, we obtain a constant-time and sub-linear space LCE query data structure.- Even when the input string is not well compressible via Lempel-Ziv 77 factorization, we still can obtain a constant-time and sub-linear space LCE data structure for suitable tau and for sigma leq 2^{o(log n)}.- The time-space trade-off lower bounds for the LCE problem by Bille et al. [J. Discrete Algorithms, 25:42-50, 2014] and by Kosolobov [CoRR, abs/1611.02891, 2016] do not apply in some cases with our LCE data structure. |
Year | Venue | Field |
|---|---|---|
2017 | MFCS | LCP array,Binary logarithm,Discrete mathematics,Data structure,Combinatorics,Computer science,Factorization,Sigma,Alphabet |
DocType | Citations | PageRank |
Conference | 1 | 0.37 |
References | Authors | |
0 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuka Tanimura | 1 | 7 | 1.55 |
| Takaaki Nishimoto | 2 | 23 | 3.54 |
| Hideo Bannai | 3 | 620 | 79.87 |
| Shunsuke Inenaga | 4 | 595 | 79.02 |
| Masayuki Takeda | 5 | 9 | 13.78 |