Results 1 to 10 of about 142,780 (319)
Hardness of the maximum-independent-set problem on unit-disk graphs and prospects for quantum speedups [PDF]
Physical Review Research, 2023 Rydberg atom arrays are among the leading contenders for the demonstration of quantum speedups. Motivated by recent experiments with up to 289 qubits [Ebadi et al., Science 376, 1209 (2022)0036-807510.1126/science.abo6587], we study the maximum ...
Ruben S. Andrist +11 more
doaj +6 more sources
Dynamic Parameterized Problems on Unit Disk Graphs [PDF]
International Symposium on Algorithms and ComputationIn this paper, we study fundamental parameterized problems such as $k$-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs.
Shinwoo An +8 more
semanticscholar +6 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 +5 more sources
Shortest Path Separators in Unit Disk Graphs [PDF]
Embedded Systems and ApplicationsWe introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices.
Elfarouk Harb +2 more
semanticscholar +6 more sources
Discrete Mathematics, 1991 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.
Brent N. Clark +2 more
semanticscholar +2 more sources
Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete [PDF]
, 2013 We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges.
J. Díaz, P. Bose, R. Tamassia
core +3 more sources
Improper colouring of (random) unit disk graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 For any graph $G$, the $k$-improper chromatic number $χ ^k(G)$ is the smallest number of colours used in a colouring of $G$ such that each colour class induces a subgraph of maximum degree $k$.
Ross J. Kang +2 more
doaj +9 more sources
Sparse hop spanners for unit disk graphs [PDF]
Computational Geometry, 2021 20 pages, 9 ...
Adrian Dumitrescu +2 more
openalex +6 more sources
A QPTAS for Facility Location on Unit Disk Graphs [PDF]
Workshop on Algorithms and Data StructuresWe study the classic \textsc{(Uncapacitated) Facility Location} problem on Unit Disk Graphs (UDGs). For a given point set $P$ in the plane, the unit disk graph UDG(P) on $P$ has vertex set $P$ and an edge between two distinct points $p, q \in P$ if and ...
Friggstad, Zachary +3 more
semanticscholar +4 more sources
A PTAS for the minimum dominating set problem in unit disk graphs [PDF]
, 2004 We present a polynomial-time approximation scheme (PTAS) for the minimum dominating set problem in unit disk graphs. In contrast to previously known approximation schemes for the minimum dominating set problem on unit disk graphs, our approach does not ...
Hurink, Johann, Nieberg, Tim
core +3 more sources