The Annals of Applied Probability

Vertex ordering and partitioning problems for random spatial graphs

Mathew D. Penrose

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 22 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1019487353

Digital Object Identifier
doi:10.1214/aoap/1019487353

Mathematical Reviews number (MathSciNet)
MR1768225

Zentralblatt MATH identifier
1052.60080

Subjects
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]

Keywords
Combinatorial optimization percolation random graphs connectivity geometric probability large deviations.

Citation

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. https://projecteuclid.org/euclid.aoap/1019487353


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