Perfect elimination orderings for symmetric matrices

Monique Laurent; Shin-ichi Tanigawa

doi:10.1007/s11590-017-1213-y

Perfect elimination orderings for symmetric matrices

Monique Laurent, Shin-ichi Tanigawa

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Abstract

We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of monotone families of chordal graphs, Robinsonian matrices and ultrametrics. We give a structural characterization for matrices that admit perfect elimination orderings in terms of forbidden substructures generalizing chordless cycles in graphs.

Original language	English
Pages (from-to)	339-353
Journal	Optimization Letters
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/s11590-017-1213-y
Publication status	Published - Mar 2020

Keywords

chordal graph
perfect elimination ordering
unit interval graph
ultrametric
shortest path metric
robinson matrix

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10.1007/s11590-017-1213-y

1 Citations
1 Working paper

Perfect Elimination Orderings for Symmetric Matrices
Laurent, M. & Tanigawa, S.-I., 17 Apr 2017, Ithaca: Cornell University Library, 17 p. (arXiv; vol. 1706.05115).
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Cite this

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title = "Perfect elimination orderings for symmetric matrices",

abstract = "We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of monotone families of chordal graphs, Robinsonian matrices and ultrametrics. We give a structural characterization for matrices that admit perfect elimination orderings in terms of forbidden substructures generalizing chordless cycles in graphs.",

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AU - Tanigawa, Shin-ichi

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AB - We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of monotone families of chordal graphs, Robinsonian matrices and ultrametrics. We give a structural characterization for matrices that admit perfect elimination orderings in terms of forbidden substructures generalizing chordless cycles in graphs.

KW - chordal graph

KW - perfect elimination ordering

KW - unit interval graph

KW - ultrametric

KW - shortest path metric

KW - robinson matrix

U2 - 10.1007/s11590-017-1213-y

DO - 10.1007/s11590-017-1213-y

M3 - Article

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VL - 14

SP - 339

EP - 353

JO - Optimization Letters

JF - Optimization Letters

IS - 2

ER -

Perfect elimination orderings for symmetric matrices

Abstract

Keywords

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Research output

Perfect Elimination Orderings for Symmetric Matrices

Cite this