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WG
1999
Springer

Linear Orderings of Random Geometric Graphs

10 years 8 months ago
Linear Orderings of Random Geometric Graphs
Abstract. In random geometric graphs, vertices are randomly distributed on [0, 1]2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.
Josep Díaz, Mathew D. Penrose, Jordi Petit,
Added 05 Aug 2010
Updated 05 Aug 2010
Type Conference
Year 1999
Where WG
Authors Josep Díaz, Mathew D. Penrose, Jordi Petit, Maria J. Serna
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