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The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…

Data Structures and Algorithms · Computer Science 2022-01-26 Yuxuan Wang , Jinyao Xie , Jiongzhi Zheng , Kun He

Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…

Computational Geometry · Computer Science 2021-11-05 Omrit Filtser , Majid Mirzanezhad , Carola Wenk

We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x…

Computational Geometry · Computer Science 2012-06-21 Laszlo Kozma

The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…

Logic in Computer Science · Computer Science 2018-05-01 Christel Baier , Nathalie Bertrand , Clemens Dubslaff , Daniel Gburek , Ocan Sankur

Let $G=(V,E)$ be any undirected graph on $V$ vertices and $E$ edges. A path $\textbf{P}$ between any two vertices $u,v\in V$ is said to be $t$-approximate shortest path if its length is at most $t$ times the length of the shortest path…

Data Structures and Algorithms · Computer Science 2010-02-03 Neelesh Khanna Surender Baswana

We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this…

Computational Geometry · Computer Science 2007-05-23 Jeff Erickson , Sariel Har-Peled

A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb N$, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size…

Data Structures and Algorithms · Computer Science 2020-10-01 Leon Kellerhals , Tomohiro Koana

Given a point set P in 2D, the problem of finding the smallest set of unit disks that cover all of P is NP-hard. We present a simple algorithm for this problem with an approximation factor of 25/6 in the Euclidean norm and 2 in the max…

Computational Geometry · Computer Science 2014-06-17 Paul Liu , Daniel Lu

Given a graph with edge costs, the {\em power} of a node is themaximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following…

Data Structures and Algorithms · Computer Science 2011-07-26 Nachshon Cohen , Zeev Nutov

The composition problem for shortest paths asks the following: given shortest paths on weighted graphs M and N which share a common boundary, find the shortest paths on their union. This problem is a crucial step in any algorithm which uses…

Discrete Mathematics · Computer Science 2022-09-07 Jade Master

This paper presents a study on two data structures that have been used to model several problems in computer science: and/or graphs and x-y graphs. An and/or graph is an acyclic digraph containing a source, such that every vertex v has a…

Computational Complexity · Computer Science 2012-03-16 Maise Dantas da Silva , Fábio Protti , Uéverton dos Santos Souza

We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit…

Computational Geometry · Computer Science 2024-04-19 Mikkel Abrahamsen , Jack Stade

Given a set $P$ of $n$ points in the plane and a collection of disks centered at these points, the disk graph $G(P)$ has vertex set $P$, with an edge between two vertices if their corresponding disks intersect. We study the dominating set…

Computational Geometry · Computer Science 2026-02-02 Anastasiia Tkachenko , Haitao Wang

In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…

Robotics · Computer Science 2022-02-25 Si Wei Feng , Jingjin Yu

The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…

Physics and Society · Physics 2026-02-05 Zhihao Qiu , Sámuel G. Balogh , Xinhan Liu , Piet Van Mieghem , Maksim Kitsak

We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are…

Optimization and Control · Mathematics 2025-11-07 Elvise Berchio , Filomena Feo , Antonio Giuseppe Grimaldi

In this paper, we deal with an obstacle placement problem inside a disk, that can be formulated as an energy minimization problem with respect to the rotations of the obstacle about its center, with respect to the translations of the…

Analysis of PDEs · Mathematics 2019-12-17 Anisa M H Chorwadwala

The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…

Data Structures and Algorithms · Computer Science 2015-06-02 Neal Young , Robert Tarjan , James Orlin

The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with…

Discrete Mathematics · Computer Science 2020-06-24 Frank Gurski , Dominique Komander , Carolin Rehs

Let $V$ be a set of $n$ points in the plane. The unit-disk graph $G = (V, E)$ has vertex set $V$ and an edge $e_{uv} \in E$ between vertices $u, v \in V$ if the Euclidean distance between $u$ and $v$ is at most 1. The weight of each edge…

Computational Geometry · Computer Science 2024-07-04 Bruce W. Brewer , Haitao Wang