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Random Geometric Graphs$
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Mathew Penrose

Print publication date: 2003

Print ISBN-13: 9780198506263

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506263.001.0001

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ORDERING AND PARTITIONING PROBLEMS

ORDERING AND PARTITIONING PROBLEMS

Chapter:
(p.259) 12 ORDERING AND PARTITIONING PROBLEMS
Source:
Random Geometric Graphs
Author(s):

Mathew Penrose (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506263.003.0012

Given an ordering of the vertices of a graph, let the induced weight for an edge be the separation of its end-points in the ordering. Layout problems involve choosing the ordering to minimize a cost functional, such as the sum or maximum of the edge-weights. A related problem is to bisect the vertex set to minimize the number of edges between the two halves of the vertex set. In this chapter, growth rates are given for the optimal costs of some of these problems on random geometric graphs in the thermodynamic limit, and precise asymptotic costs are given in the superconnective limiting regime.

Keywords:   ordering of vertices, bisect, optimal costs, thermodynamic limit, phase transition, superconnective limiting regime

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