Results 1 to 10 of about 89,734 (93)
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
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Quantum Optimization with Arbitrary Connectivity Using Rydberg Atom Arrays
PRX Quantum, 2023 Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits.
Minh-Thi Nguyen +5 more
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Case Studies in Thermal Engineering, 2022 This research article concentrates on forced convection with a high Reynolds number of the water-alumina-based nanofluid in the square cavity containing a rotating disk with a unit speed. A very dense mesh is used to obtain the numerical results with the
Usman +6 more
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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
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QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs [PDF]
, 2018 A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since
Bonnet, E. +4 more
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Good quality virtual realization of unit disk graphs
Journal of Computational Geometry, 2011 We consider the problem of finding a realization of an n-vertex unit disk graph (UDG) expressed in general form, say, as an adjacency matrix. The problem is to construct an embedding of the graph in low-dimensional Euclidean space so that the ratio of ...
Sriram Pemmaraju, Imran Pirwani
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Impact of Locality on Location Aware Unit Disk Graphs
Algorithms, 2008 Due to their importance for studies oi wireless networks, recent years have seen a surge of activity on the design of local algorithms for the solution of a variety of network tasks. We study the behaviour of algorithms with very low localities.
Evangelos Kranakis, Andreas Wiese
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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
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Local Approximation Schemes for Ad Hoc and Sensor Networks [PDF]
, 2005 We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs.
Kuhn, F. +3 more
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On isolating points using unit disks
Journal of Computational Geometry, 2016 Given a set of points in the plane and a set of disks (that we think of as wireless sensors) which separate the points, we consider the problem of selecting a minimum subset of the disks such that any path between any pair of points is intersected by at ...
Matt Gibson +4 more
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