Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1902.00216

An Extension of Linear-size Suffix Tries for Parameterized Strings

Katsuhito Nakashima·Diptarama Hendrian·Ryo Yoshinaka·Ayumi Shinohara
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we propose a new indexing structure for parameterized strings which we call PLSTs, by generalizing linear-size suffix tries for ordinary strings. Two parameterized strings are said to match if there is a bijection on the symbol set that makes the two coincide. PLSTs are applicable to the parameterized pattern matching problem, which is to decide whether the input parameterized text has a substring that matches the input parameterized pattern. The size of PLSTs is linear in the text size, with which our algorithm solves the parameterized pattern matching problem in linear time in the pattern size. PLSTs can be seen as a compacted version of parameterized suffix tries and a combination of linear-size suffix tries and parameterized suffix trees. We experimentally show that PLSTs are more space efficient than parameterized suffix trees for highly repetitive strings.

Explore related subjects

cs.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Katsuhito Nakashima, Diptarama Hendrian, Ryo Yoshinaka, Ayumi Shinohara. 2019-09-04. An Extension of Linear-size Suffix Tries for Parameterized Strings. https://arxiv.org/abs/1902.00216

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗