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We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it…

Logic in Computer Science · Computer Science 2015-07-01 Wojciech Kazana , Luc Segoufin

Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…

Computational Geometry · Computer Science 2022-08-29 Vaclav Skala

A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. Variants of this problem have seen…

Data Structures and Algorithms · Computer Science 2026-04-03 Jackson Bibbens , Levi Borevitz , Samuel McCauley

Many search engines such as Google, Bing & Yahoo! show search suggestions when users enter search phrases on their interfaces. These suggestions are meant to assist the user in finding what she wants quickly and also suggesting common…

Data Structures and Algorithms · Computer Science 2021-11-01 Dhruv Matani

Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these conditions in the log-domain is a natural variation on this approach that to our knowledge is…

Optimization and Control · Mathematics 2022-12-06 Frank Permenter

In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high…

Data Structures and Algorithms · Computer Science 2015-03-13 Michael T. Goodrich

Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously…

Data Structures and Algorithms · Computer Science 2014-04-23 Omer Reingold , Shai Vardi

We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a…

Computational Geometry · Computer Science 2025-05-12 Jonathan E. Dullerud , Sariel Har-Peled

Let $P$ be a set of $n$ points in the plane. We consider the problem of partitioning $P$ into two subsets $P_1$ and $P_2$ such that the sum of the perimeters of $\text{CH}(P_1)$ and $\text{CH}(P_2)$ is minimized, where $\text{CH}(P_i)$…

Computational Geometry · Computer Science 2021-03-02 Mikkel Abrahamsen , Mark de Berg , Kevin Buchin , Mehran Mehr , Ali D. Mehrabi

We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…

Data Structures and Algorithms · Computer Science 2018-09-28 Klaus Jansen , Marten Maack , Alexander Mäcker

For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…

Data Structures and Algorithms · Computer Science 2016-02-01 Tomasz Kociumaka

Given an $n$-vertex planar embedded digraph $G$ with non-negative edge weights and a face $f$ of $G$, Klein presented a data structure with $O(n\log n)$ space and preprocessing time which can answer any query $(u,v)$ for the shortest path…

Data Structures and Algorithms · Computer Science 2023-07-31 Debarati Das , Evangelos Kipouridis , Maximilian Probst Gutenberg , Christian Wulff-Nilsen

Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that…

Databases · Computer Science 2024-10-23 Luis Croquevielle , Guang Yang , Liang Liang , Ali Hadian , Thomas Heinis

Whenever eye movements are measured, a central part of the analysis has to do with where subjects fixate, and why they fixated where they fixated. To a first approximation, a set of fixations can be viewed as a set of points in space: this…

Applications · Statistics 2013-05-23 Simon Barthelmé , Hans Trukenbrod , Ralf Engbert , Felix Wichmann

In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…

Computational Geometry · Computer Science 2014-06-26 Luis Barba , Matias Korman , Stefan Langerman , Kunikiko Sadakane , Rodrigo Silveira

Predicting how the world can evolve in the future is crucial for motion planning in autonomous systems. Classical methods are limited because they rely on costly human annotations in the form of semantic class labels, bounding boxes, and…

Computer Vision and Pattern Recognition · Computer Science 2023-05-02 Tarasha Khurana , Peiyun Hu , David Held , Deva Ramanan

We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…

Data Structures and Algorithms · Computer Science 2026-05-06 Bernhard Haeupler , Richard Hladík , John Iacono , Vaclav Rozhon , Robert Tarjan , Jakub Tětek

An algorithm is presented to compute isolated values of the divisor summatory function in O(n^(1/3)) time and O (log n) space. The algorithm is elementary and uses a geometric approach of successive approximation combined with coordinate…

Number Theory · Mathematics 2012-06-18 Richard Sladkey

We consider the $\mathcal{NP}$-hard problem $\mathrm{P} \mathbf{\vert} \mathrm{pmtn, setup=s_i} \mathbf{\vert} \mathrm{C_{\max}}$, the problem of scheduling $n$ jobs, which are divided into $c$ classes, on $m$ identical parallel machines…

Data Structures and Algorithms · Computer Science 2025-08-21 Max A. Deppert , David Fischer , Klaus Jansen

Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…

Computational Geometry · Computer Science 2016-07-20 Ingo van Duijn , Irina Kostitsyna , Marc van Kreveld , Maarten Löffler