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Given two convex polygons $P$ and $Q$ with $n$ and $m$ edges, the maximum overlap problem is to find a translation of $P$ that maximizes the area of its intersection with $Q$. We give the first randomized algorithm for this problem with…

Computational Geometry · Computer Science 2025-04-28 Timothy M. Chan , Isaac M. Hair

We present new refinement heuristics for the balanced graph partitioning problem that break with an age-old rule. Traditionally, local search only permits moves that keep the block sizes balanced (below a size constraint). In this work, we…

Social and Information Networks · Computer Science 2025-05-13 Nikolai Maas , Lars Gottesbüren , Daniel Seemaier

We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of $\mathbb{R}^d$ (including advection equations on surfaces)…

Numerical Analysis · Mathematics 2025-08-15 Thomas Hangelbroek , Christian Rieger , Grady B. Wright

We develop, analyze, implement, and compare new algorithms for creating $\varepsilon$-samples of range spaces defined by halfspaces which have size sub-quadratic in $1/\varepsilon$, and have runtime linear in the input size and…

Computational Geometry · Computer Science 2018-07-19 Michael Matheny , Jeff M. Phillips

In the Area Labeling Problem one is after placing the label of a geographic area. Given the outer boundary of the area and an optional set of holes. The goal is to find a label position such that the label spans the area and is conform to…

Human-Computer Interaction · Computer Science 2020-01-10 Filip Krumpe , Thomas Mendel

We study the optimization version of the equal cardinality set partition problem (where the absolute difference between the equal sized partitions' sums are minimized). While this problem is NP-hard and requires exponential complexity to…

Data Structures and Algorithms · Computer Science 2021-09-17 Kaan Gokcesu , Hakan Gokcesu

It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…

General Mathematics · Mathematics 2007-05-23 Aleksandr Golubchik

Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that…

Optimization and Control · Mathematics 2017-09-27 Yonatan Mintz , Anil Aswani

We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering…

Data Structures and Algorithms · Computer Science 2015-04-22 Dániel Marx , Michał Pilipczuk

The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on…

Data Structures and Algorithms · Computer Science 2015-09-16 Petr A. Golovach , Pinar Heggernes , Mamadou Moustapha Kanté , Dieter Kratsch , Sigve H. Sæther , Yngve Villanger

In the imprecise geometry model, the input is an imprecise point set, which is a family of regions $F = (R_1, \ldots,R_n)$, where for each $R_i$ one may retrieve the true point $p_i \in R_i$. By preprocessing $F$, we can construct the…

Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…

Computational Geometry · Computer Science 2019-03-13 Benjamin Niedermann , Ignaz Rutter , Matthias Wolf

Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles,…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-04-14 Erik Saule , Erdeniz Ö. Baş , Ümit V. Çatalyürek

Let $S$ be a planar $n$-point set. A triangulation for $S$ is a maximal plane straight-line graph with vertex set $S$. The Voronoi diagram for $S$ is the subdivision of the plane into cells such that all points in a cell have the same…

Computational Geometry · Computer Science 2020-10-05 Matias Korman , Wolfgang Mulzer , Andre van Renssen , Marcel Roeloffzen , Paul Seiferth , Yannik Stein

We give the first truly subquadratic time algorithm, with $O^*(n^{2-1/18})$ running time, for computing the diameter of an $n$-vertex unit-disk graph, resolving a central open problem in the literature. Our result is obtained as an instance…

Data Structures and Algorithms · Computer Science 2025-10-21 Timothy M. Chan , Hsien-Chih Chang , Jie Gao , Sándor Kisfaludi-Bak , Hung Le , Da Wei Zheng

We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…

Data Structures and Algorithms · Computer Science 2019-08-13 Sven Mallach

The weighted $\mathcal{T}$-free $2$-matching problem is the following problem: given an undirected graph $G$, a weight function on its edge set, and a set $\mathcal{T}$ of triangles in $G$, find a maximum weight $2$-matching containing no…

Data Structures and Algorithms · Computer Science 2019-11-18 Yusuke Kobayashi

Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…

Data Structures and Algorithms · Computer Science 2024-06-12 Ziao Wang , Weina Wang , Lele Wang

A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by…

Data Structures and Algorithms · Computer Science 2017-11-08 Yoichi Iwata , Yutaro Yamaguchi , Yuichi Yoshida

The polygon retrieval problem on points is the problem of preprocessing a set of $n$ points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great interest in areas such…

Computational Geometry · Computer Science 2009-07-30 Spyros Sioutas , Dimitrios Sofotassios , Kostas Tsichlas , Dimitrios Sotiropoulos , Panayiotis Vlamos