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On a class of metrics related to graph layout problems

Letchford, A N and Reinelt, G and Seitz, H and Theis, D O (2010) On a class of metrics related to graph layout problems. Linear Algebra and its Applications, 433 (11-12). pp. 1760-1777.

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    Abstract

    We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the literature, and also to a class of combinatorial optimization problems known as graph layout problems. We prove several results about the structure of these metrics. In particular, it is shown that their convex hull is not closed in general. We then show that certain linear inequalities define facets of the closure of the convex hull. Finally, we characterize the unbounded edges of the convex hull and of its closure.

    Item Type: Article
    Journal or Publication Title: Linear Algebra and its Applications
    Uncontrolled Keywords: metric spaces ; graph layout problems ; convex analysis ; polyhedral combinatorics
    Subjects: H Social Sciences > HB Economic Theory
    Departments: Lancaster University Management School > Management Science
    ID Code: 45623
    Deposited By: ep_importer_pure
    Deposited On: 11 Jul 2011 19:35
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Apr 2014 22:35
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/45623

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