arXiv subjects

Kazuya Tsuruta

Publications and source records attributed to Kazuya Tsuruta.

3 recordsLinked to original sources

arXiv2020

c-trie++: A Dynamic Trie Tailored for Fast Prefix Searches

Given a dynamic set $K$ of $k$ strings of total length $n$ whose characters are drawn from an alphabet of size $σ$, a keyword dictionary is a data structure built on $K$ that provides locate, prefix search, and update operations on $K$. Under the assumption that $α= w / \lg σ$ characters fit into a single machine word $w$, we propose a keyword dictionary that represents $K$ in $n \lg σ+ Θ(k \lg n)$ bits of space, supporting all operations in $O(m / α+ \lg α)$ expected time on an input string of length $m$ in the word RAM model. This data structure is underlined with an exhaustive practical evaluation, highlighting the practical usefulness of the proposed data structure, especially for prefix searches - one of the most elementary keyword dictionary operations.

cs.DS↗

arXiv2020

Grammar-compressed Self-index with Lyndon Words

We introduce a new class of straight-line programs (SLPs), named the Lyndon SLP, inspired by the Lyndon trees (Barcelo, 1990). Based on this SLP, we propose a self-index data structure of $O(g)$ words of space that can be built from a string $T$ in $O(n \lg n)$ expected time, retrieving the starting positions of all occurrences of a pattern $P$ of length $m$ in $O(m + \lg m \lg n + occ \lg g)$ time, where $n$ is the length of $T$, $g$ is the size of the Lyndon SLP for $T$, and $occ$ is the number of occurrences of $P$ in $T$.

cs.DS↗

arXiv2015

The "Runs" Theorem

We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon words. The characterization leads to a proof of what was known as the "runs" conjecture (Kolpakov \& Kucherov (FOCS '99)), which states that the maximum number of runs $ρ(n)$ in a string of length $n$ is less than $n$. The proof is remarkably simple, considering the numerous endeavors to tackle this problem in the last 15 years, and significantly improves our understanding of how runs can occur in strings. In addition, we obtain an upper bound of $3n$ for the maximum sum of exponents $σ(n)$ of runs in a string of length $n$, improving on the best known bound of $4.1n$ by Crochemore et al. (JDA 2012), as well as other improved bounds on related problems. The characterization also gives rise to a new, conceptually simple linear-time algorithm for computing all the runs in a string. A notable characteristic of our algorithm is that, unlike all existing linear-time algorithms, it does not utilize the Lempel-Ziv factorization of the string. We also establish a relationship between runs and nodes of the Lyndon tree, which gives a simple optimal solution to the 2-Period Query problem that was recently solved by Kociumaka et al. (SODA 2015).

cs.DM↗