The Annals of Applied Probability

Vertex ordering and partitioning problems for random spatial graphs

Mathew D. Penrose

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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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Ann. Appl. Probab., Volume 10, Number 2 (2000), 517-538.

First available in Project Euclid: 22 April 2002

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Zentralblatt MATH identifier

Primary: 05C78: Graph labelling (graceful graphs, bandwidth, etc.) 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 05C80: Random graphs [See also 60B20] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Combinatorial optimization percolation random graphs connectivity geometric probability large deviations.


Penrose, Mathew D. Vertex ordering and partitioning problems for random spatial graphs. Ann. Appl. Probab. 10 (2000), no. 2, 517--538. doi:10.1214/aoap/1019487353.

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