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» Dispersion in Unit Disks
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WG
2004
Springer
13 years 10 months ago
A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs
A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum weight independent set problem i...
Tim Nieberg, Johann Hurink, Walter Kern
STOC
1996
ACM
95views Algorithms» more  STOC 1996»
13 years 9 months ago
Pushing Disks Together - The Continuous-Motion Case
If disks are moved so that each center
Marshall W. Bern, Amit Sahai
APPROX
2006
Springer
234views Algorithms» more  APPROX 2006»
13 years 9 months ago
Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs
For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph...
Christoph Ambühl, Thomas Erlebach, Matú...
CORR
2006
Springer
134views Education» more  CORR 2006»
13 years 5 months ago
Max-Cut and Max-Bisection are NP-hard on unit disk graphs
We prove that the max-cut and max-bisection problems are NP-hard on unit disk graphs. We also show that -precision graphs are planar for > 1/ 2 and give a dichotomy theorem f...
Josep Díaz, Marcin Kaminski
WG
2010
Springer
13 years 3 months ago
The Number of Bits Needed to Represent a Unit Disk Graph
We prove that for sufficiently large n, there exist unit disk graphs on n vertices such that for every representation with disks in the plane at least c √ n bits are needed to wr...
Colin McDiarmid, Tobias Müller