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The modular subset sum problem consists of deciding, given a modulus $m$, a multiset $S$ of $n$ integers in $0..m-1$, and a target integer $t$, whether there exists a subset of $S$ with elements summing to $t \mod m $, and to report such a…

Data Structures and Algorithms · Computer Science 2023-10-27 Jean Cardinal , John Iacono

We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of $d$ strings of length $m$ and an integer $k$, we must preprocess it into a data structure to answer the following queries: Given a query…

Data Structures and Algorithms · Computer Science 2018-06-27 Paweł Gawrychowski , Gad M. Landau , Tatiana Starikovskaya

Dynamic resource allocation problems are ubiquitous, arising in inventory management, order fulfillment, online advertising, and other applications. We initially focus on one of the simplest models of online resource allocation: the…

Probability · Mathematics 2025-06-04 Omar Besbes , Yash Kanoria , Akshit Kumar

Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l;…

Databases · Computer Science 2008-11-19 Rasmus Pagh , S. Srinivasa Rao

This paper introduces a new data-structural object that we call the tiny pointer. In many applications, traditional $\log n $-bit pointers can be replaced with $o (\log n )$-bit tiny pointers at the cost of only a constant-factor time…

Data Structures and Algorithms · Computer Science 2021-11-29 Michael A. Bender , Alex Conway , Martín Farach-Colton , William Kuszmaul , Guido Tagliavini

We consider a fundamental problem in data structures, static predecessor searching: Given a subset S of size n from the universe [m], store S so that queries of the form "What is the predecessor of x in S?" can be answered efficiently. We…

Computational Complexity · Computer Science 2007-05-23 Pranab Sen , S. Venkatesh

We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…

Data Structures and Algorithms · Computer Science 2007-05-23 Stephen Alstrup , Jacob Holm , Kristian de Lichtenberg , Mikkel Thorup

Given a static reference string $R$ and a source string $S$, a relative compression of $S$ with respect to $R$ is an encoding of $S$ as a sequence of references to substrings of $R$. Relative compression schemes are a classic model of…

Data Structures and Algorithms · Computer Science 2016-09-19 Philip Bille , Patrick Hagge Cording , Inge Li Gørtz , Frederik Rye Skjoldjensen , Hjalte Wedel Vildhøj , Søren Vind

In this paper we present an implicit dynamic dictionary with the working-set property, supporting insert(e) and delete(e) in O(log n) time, predecessor(e) in O(log l_{p(e)}) time, successor(e) in O(log l_{s(e)}) time and search(e) in O(log…

Data Structures and Algorithms · Computer Science 2012-07-05 Gerth Stølting Brodal , Casper Kejlberg-Rasmussen

This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…

Data Structures and Algorithms · Computer Science 2013-06-04 Amihood Amir , Gianni Franceschini , Roberto Grossi , Tsvi Kopelowitz , Moshe Lewenstein , Noa Lewenstein

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

Data Structures and Algorithms · Computer Science 2018-12-24 Nicola Prezza

We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…

Data Structures and Algorithms · Computer Science 2025-02-11 Michael Emmerich

In this paper, we present a new data structure called the packed compact trie (packed c-trie) which stores a set $S$ of $k$ strings of total length $n$ in $n \log\sigma + O(k \log n)$ bits of space and supports fast pattern matching queries…

Data Structures and Algorithms · Computer Science 2017-10-11 Takuya Takagi , Shunsuke Inenaga , Kunihiko Sadakane , Hiroki Arimura

The move structure represents a permutation $\pi$ of $[0,n)$ as a covering set of $O(r)$ disjoint intervals (contiguous subsets of $[0,n)$), where $r$ is the minimum number of intervals whose values permute together. Formally, $r = 1 +…

Data Structures and Algorithms · Computer Science 2026-04-27 Nathaniel K. Brown , Ahsan Sanaullah , Shaojie Zhang , Ben Langmead

Given a set $P$ of coloured points on the real line, we study the problem of answering range $\alpha$-majority (or "heavy hitter") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to…

Data Structures and Algorithms · Computer Science 2012-12-05 Amr Elmasry , Meng He , J. Ian Munro , Patrick K. Nicholson

Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works…

Data Structures and Algorithms · Computer Science 2023-08-24 Luiz Fernando Afra Brito , Marcelo Keese Albertini , Bruno Augusto Nassif Travençolo , Gonzalo Navarro

Data structures that realize a dictionary are characterized by three basic instructions: (1) Insert (a new entry <key,value>). (2) Search by a key, returning the associated value. (3) Delete an entry. Known realizations are hashing schemes…

Logic · Mathematics 2016-09-06 Josef Schoenbrunner

We introduce a new dynamic data structure for maintaining the strongly connected components (SCCs) of a directed graph (digraph) under edge deletions, so as to answer a rich repertoire of connectivity queries. Our main technical…

Data Structures and Algorithms · Computer Science 2018-03-02 Loukas Georgiadis , Thomas Dueholm Hansen , Giuseppe F. Italiano , Sebastian Krinninger , Nikos Parotsidis

We consider the classical problem of representing a collection of priority queues under the operations \Findmin{}, \Insert{}, \Decrease{}, \Meld{}, \Delete{}, and \Deletemin{}. In the comparison-based model, if the first four operations are…

Data Structures and Algorithms · Computer Science 2011-12-06 Amr Elmasry , Jyrki Katajainen

Indexing highly repetitive texts - such as genomic databases, software repositories and versioned text collections - has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts…

Data Structures and Algorithms · Computer Science 2020-12-17 Travis Gagie , Gonzalo Navarro , Nicola Prezza