Results 11 to 20 of about 89,804 (156)
Discrete Mathematics, 1990 Any given \(n\) points in the plane form the vertices of some graph by the convention that distinct points are adjacent whenever their distance is at most 2. The resulting graph is called a unit disk graph, since it is the intersection graph of the unit disks around the given \(n\) points.
Clark, Brent N. +2 more
openaire +3 more sources
Simple heuristics for unit disk graphs [PDF]
Networks, 1995 AbstractUnit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP‐hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring, and minimum dominating set.
Marathe, M. V. +4 more
openaire +3 more sources
Maxclique and Unit Disk Characterizations of Strongly Chordal Graphs
Discussiones Mathematicae Graph Theory, 2014 Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations of chordal graphs into two new ...
Caria Pablo De, McKee Terry A.
doaj +4 more sources
On Forbidden Induced Subgraphs for Unit Disk Graphs [PDF]
Discrete & Computational Geometry, 2018 A unit disk graph is the intersection graph of disks of equal radii in the plane. The class of unit disk graphs is hereditary, and therefore admits a characterization in terms of minimal forbidden induced subgraphs. In spite of quite active study of unit disk graphs very little is known about minimal forbidden induced subgraphs for this class. We found
Aistis Atminas, Viktor Zamaraev
openaire +5 more sources
Unit Disk Visibility Graphs [PDF]
, 2021 We study unit disk visibility graphs, where the visibility relation between a pair of geometric entities is defined by not only obstacles, but also the distance between them. That is, two entities are not mutually visible if they are too far apart, regardless of having an obstacle between them.
��a����r��c��, Onur +1 more
openaire +3 more sources
Liar's domination in unit disk graphs [PDF]
Theoretical Computer Science, 2020 In this article, we study a variant of the minimum dominating set problem known as the minimum liar's dominating set (MLDS) problem. We prove that the MLDS problem is NP-hard in unit disk graphs. Next, we show that the recent sub-quadratic time $\frac{11}{2}$-factor approximation algorithm \cite{bhore} for the MLDS problem is erroneous and propose a ...
Ramesh K. Jallu +2 more
openaire +3 more sources
Routing in Unit Disk Graphs [PDF]
Algorithmica, 2016 Let $S \subset \mathbb{R}^2$ be a set of $n$ sites. The unit disk graph $\text{UD}(S)$ on $S$ has vertex set $S$ and an edge between two distinct sites $s,t \in S$ if and only if $s$ and $t$ have Euclidean distance $|st| \leq 1$. A routing scheme $R$ for $\text{UD}(S)$ assigns to each site $s \in S$ a label $\ell(s)$ and a routing table $ (s)$.
Haim Kaplan +3 more
openaire +3 more sources
Location Oblivious Distributed Unit Disk Graph Coloring [PDF]
Algorithmica, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barbeau, Michel +4 more
openaire +1 more source
Sparse hop spanners for unit disk graphs
Computational Geometry, 2022 20 pages, 9 ...
Adrian Dumitrescu +2 more
openaire +5 more sources
Minimum Clique Partition in Unit Disk Graphs [PDF]
Graphs and Combinatorics, 2011 Comment: 12 pages, 3 ...
Dumitrescu, Adrian, Pach, János
openaire +3 more sources