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In Gapped String Indexing, the goal is to compactly represent a string $S$ of length $n$ such that for any query consisting of two strings $P_1$ and $P_2$, called patterns, and an integer interval $[\alpha, \beta]$, called gap range, we can…

Data Structures and Algorithms · Computer Science 2024-03-06 Philip Bille , Inge Li Gørtz , Moshe Lewenstein , Solon P. Pissis , Eva Rotenberg , Teresa Anna Steiner

Define Minimum Soapy Union (MinSU) as the following optimization problem: given a $k$-tuple $(X_1, X_2,..., X_k)$ of finite integer sets, find a $k$-tuple $(t_1, t_2,..., t_k)$ of integers that minimizes the cardinality of $(X_1 + t_1) \cup…

Computational Complexity · Computer Science 2012-04-23 Francois Nicolas , Sebastian Böcker

We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results.…

Data Structures and Algorithms · Computer Science 2011-08-19 Philip Bille , Inge Li Goertz

Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for…

Data Structures and Algorithms · Computer Science 2019-12-04 Jarno Alanko , Tuukka Norri

We give a sublinear quantum algorithm for the longest common substring (LCS) problem on the run-length encoded (RLE) inputs, under the assumption that the prefix-sums of the runs are given. Our algorithm costs $\tilde{O}(n^{5/6})\cdot…

Quantum Physics · Physics 2023-10-03 Tzu-Ching Lee , Han-Hsuan Lin

This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…

The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…

Data Structures and Algorithms · Computer Science 2025-05-30 Rachel Cummings , Alessandro Epasto , Jieming Mao , Tamalika Mukherjee , Tingting Ou , Peilin Zhong

The {\em shortest common superstring} and the {\em shortest common supersequence} are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the…

Data Structures and Algorithms · Computer Science 2010-06-29 Raphaël Clifford , Zvi Gotthilf , Moshe Lewenstein , Alexandru Popa

The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…

Data Structures and Algorithms · Computer Science 2023-09-06 Domenico Cantone , Simone Faro , Arianna Pavone , Caterina Viola

Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…

Data Structures and Algorithms · Computer Science 2022-11-11 Philip Bille , Inge Li Gørtz , Tord Stordalen

Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$…

Data Structures and Algorithms · Computer Science 2014-06-10 Pawel Gawrychowski , Damian Rusak

We present a polynomial time algorithm, which solves a nonstandard Variation of the well-known PARTITION-problem: Given positive integers $n, k$ and $t$ such that $t \geq n$ and $k \cdot t = {n+1 \choose 2}$, the algorithm partitions the…

Combinatorics · Mathematics 2023-06-22 Alexander Büchel , Ulrich Gilleßen , Kurt-Ulrich Witt

Given a set $S$ of $n$ (distinct) keys from key space $[U]$, each associated with a value from $\Sigma$, the \emph{static dictionary} problem asks to preprocess these (key, value) pairs into a data structure, supporting value-retrieval…

Data Structures and Algorithms · Computer Science 2020-09-01 Huacheng Yu

Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…

Data Structures and Algorithms · Computer Science 2020-10-28 Karl Bringmann , Vasileios Nakos

We spot a hole in the area of succinct data structures for graph classes from a universe of size at most $n^n$. Very often, the input graph is labeled by the user in an arbitrary and easy-to-use way, and the data structure for the graph…

Data Structures and Algorithms · Computer Science 2023-11-07 Sankardeep Chakraborty , Christian Engels , Seungbum Jo , Mingmou Liu

Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences…

Data Structures and Algorithms · Computer Science 2013-11-20 Sebastian Deorowicz , Szymon Grabowski

We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only $O(s)$ words of workspace in addition to the memory for input. In this…

Computational Geometry · Computer Science 2018-04-11 Eunjin Oh , Hee-Kap Ahn

The choice dictionary is introduced as a data structure that can be initialized with a parameter $n\in\mathbb{N}=\{1,2,\ldots\}$ and subsequently maintains an initially empty subset $S$ of $\{1,\ldots,n\}$ under insertion, deletion,…

Data Structures and Algorithms · Computer Science 2017-03-17 Torben Hagerup , Frank Kammer

A closed string $u$ is either of length one or contains a border that occurs only as a prefix and as a suffix in $u$ and nowhere else within $u$. In this paper, we present fast $\mathcal{O}(n\log n)$ time algorithms to compute all…

Data Structures and Algorithms · Computer Science 2026-01-12 Samkith K Jain , Neerja Mhaskar

Given an array A containing arbitrary (positive and negative) numbers, we consider the problem of supporting range maximum-sum segment queries on A: i.e., given an arbitrary range [i,j], return the subrange [i' ,j' ] \subseteq [i,j] such…

Data Structures and Algorithms · Computer Science 2015-06-12 Pawel Gawrychowski , Patrick K. Nicholson