Small-Space LCE Data Structure with Constant-Time Queries

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

28th Annual Symposium on Combinatorial Pattern Matching : CPM 2017, July 4-6, 2017, Warsaw, Poland

Peer reviewe

Counting Maximal-Exponent Factors in Words

This article shows tight upper and lower bounds on the number of occurrences of maximal-exponent factors occurring in a word