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We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…

Data Structures and Algorithms · Computer Science 2022-12-06 Nick Fagan , Jorge Hermo González , Travis Gagie

Let $\Sigma$ and $\Pi$ be disjoint alphabets, respectively called the static alphabet and the parameterized alphabet. Two strings $x$ and $y$ over $\Sigma \cup \Pi$ of equal length are said to parameterized match (p-match) if there exists a…

Data Structures and Algorithms · Computer Science 2021-02-05 Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and…

Data Structures and Algorithms · Computer Science 2013-01-15 Travis Gagie , Wing-Kai Hon , Tsung-Han Ku

We consider the problem of representing, in a compressed format, a bit-vector $S$ of $m$ bits with $n$ 1s, supporting the following operations, where $b \in \{0, 1 \}$: $rank_b(S,i)$ returns the number of occurrences of bit $b$ in the…

Data Structures and Algorithms · Computer Science 2009-02-17 Roberto Grossi , Alessio Orlandi , Rajeev Raman , S. Srinivasa Rao

Time series are ubiquitous in domains ranging from medicine to marketing and finance. Frequent Pattern Mining (FPM) from a time series has thus received much attention. Recently, it has been studied under the order-preserving (OP) matching…

Data Structures and Algorithms · Computer Science 2024-12-02 Ling Li , Wiktor Zuba , Grigorios Loukides , Solon P. Pissis , Maria Matsangidou

We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern $P[1 .. m]$ on a large repetitive text collection $T[1 .. n]$, which is represented as a (hopefully much smaller) run-length context-free grammar of…

Data Structures and Algorithms · Computer Science 2023-09-06 Gonzalo Navarro

Assuming we are in a Word-RAM model with word size $w$, we show that we can construct in $o(w)$ time an error correcting code with a constant relative positive distance that maps numbers of $w$ bits into $\Theta(w)$-bit numbers, and such…

Data Structures and Algorithms · Computer Science 2014-09-16 Djamal Belazzougui

Given a string $T$ of length $n$ over an alphabet $\Sigma\subset \{1,2,\ldots,n^{O(1)}\}$ of size $\sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $\Sigma$ that is…

Data Structures and Algorithms · Computer Science 2021-06-04 Golnaz Badkobeh , Panagiotis Charalampopoulos , Dmitry Kosolobov , Solon P. Pissis

Grammar compression is a general compression framework in which a string $T$ of length $N$ is represented as a context-free grammar of size $n$ whose language contains only $T$. In this paper, we focus on studying the limitations of…

Data Structures and Algorithms · Computer Science 2024-09-24 Rajat De , Dominik Kempa

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…

Data Structures and Algorithms · Computer Science 2019-08-14 Benjamin Aram Berendsohn , László Kozma , Dániel Marx

Given a planar map of $n$ segments in which we wish to efficiently locate points, we present the first randomized incremental construction of the well-known trapezoidal-map search-structure that only requires expected $O(n \log n)$…

Computational Geometry · Computer Science 2014-10-22 Michael Hemmer , Michal Kleinbort , Dan Halperin

In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once.…

Data Structures and Algorithms · Computer Science 2009-06-26 Paolo Ferragina , Igor Nitto , Rossano Venturini

We consider the problem of constructing a sparse suffix tree (or suffix array) for $b$ suffixes of a given text $T$ of size $n$, using only $O(b)$ words of space during construction time. Breaking the naive bound of $\Omega(nb)$ time for…

Data Structures and Algorithms · Computer Science 2012-07-06 Philip Bille , Inge Li Gørtz , Tsvi Kopelowitz , Benjamin Sach , Hjalte Wedel Vildhøj

Given a string $S$, the \emph{compressed indexing problem} is to preprocess $S$ into a compressed representation that supports fast \emph{substring queries}. The goal is to use little space relative to the compressed size of $S$ while…

Data Structures and Algorithms · Computer Science 2018-01-10 Philip Bille , Mikko Berggren Ettienne , Inge Li Gørtz , Hjalte Wedel Vildhøj

The suffix tree is a very important data structure in string processing, but it suffers from a huge space consumption. In large-scale applications, compressed suffix trees (CSTs) are therefore used instead. A CST consists of three…

Data Structures and Algorithms · Computer Science 2010-12-21 Simon Gog , Enno Ohlebusch

Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…

Data Structures and Algorithms · Computer Science 2016-09-01 Shouhei Fukunaga , Yoshimasa Takabatake , I Tomohiro , Hiroshi Sakamoto

We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path $\alpha$-minority queries. We present the first linear-space data structures, requiring $O(n…

Data Structures and Algorithms · Computer Science 2026-04-22 Ovidiu Rata

We propose a B tree representation storing $n$ keys, each of $k$ bits, in either (a) $nk + O(nk / \lg n)$ bits or (b) $nk + O(nk \lg \lg n/ \lg n)$ bits of space supporting all B tree operations in either (a) $O(\lg n )$ time or (b) $O(\lg…

Data Structures and Algorithms · Computer Science 2021-04-20 Tomohiro I , Dominik Köppl

For the first time we provide a succinct pattern matching index for arbitrary graphs that can be built in polynomial time, which requires less space and answers queries more efficiently than the one in [SODA 2021]. We show that, given an…

Data Structures and Algorithms · Computer Science 2021-11-09 Nicola Cotumaccio

We present the first linear time algorithm to construct the $2n$-bit version of the Lyndon array for a string of length $n$ using only $o(n)$ bits of working space. A simpler variant of this algorithm computes the plain ($n\lg n$-bit)…

Data Structures and Algorithms · Computer Science 2019-12-11 Philip Bille , Jonas Ellert , Johannes Fischer , Inge Li Gørtz , Florian Kurpicz , Ian Munro , Eva Rotenberg