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May 2000 Vertex ordering and partitioning problems for random spatial graphs
Mathew D. Penrose
Ann. Appl. Probab. 10(2): 517-538 (May 2000). DOI: 10.1214/aoap/1019487353


Given an ordering of the vertices of a finite graph, let the induced weight for an edge be the separation of its endpoints in the ordering. Layout problems involve choosing the ordering to minimize a cost functional such as the sum or maximum of the edge weights. We give growth rates for the costs of some of these problems on supercritical percolation processes and supercritical random geometric graphs, obtained by placing vertices randomly in the unit cube and joining them whenever at most some threshold distance apart.


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Mathew D. Penrose. "Vertex ordering and partitioning problems for random spatial graphs." Ann. Appl. Probab. 10 (2) 517 - 538, May 2000.


Published: May 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1052.60080
MathSciNet: MR1768225
Digital Object Identifier: 10.1214/aoap/1019487353

Primary: 05C78 , 60D05
Secondary: 05C80 , 60K35

Keywords: Combinatorial optimization , connectivity , geometric probability , large deviations. , percolation , Random graphs

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 2 • May 2000
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