Publication: An Optimization-Based Sum-of-Squares Ap...
Master data
Title: | An Optimization-Based Sum-of-Squares Approach to Vizing's Conjecture |
Subtitle: | |
Abstract: | Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formulate Vizing's conjecture itself as a Positivstellensatz existence question. In particular, we encode the conjecture as an ideal/polynomial pair such that the polynomial is nonnegative if and only if the conjecture is true. We demonstrate how to use semidefinite optimization techniques to computationally obtain numeric sum-of-squares certificates, and then show how to transform these numeric certificates into symbolic certificates approving nonnegativity of our polynomial. After outlining the theoretical structure of this computer-based proof of Vizing's conjecture, we present computational and theoretical results. In particular, we present exact low-degree sparse sum-of-squares certificates for particular families of graphs. |
Keywords: | Vizing’s conjecture; algebraic model; Gröbner basis; sum-of-squaresproblems; semidefinite programming |
Publication type: | Article in Proceedings (Authorship) |
Publication date: | 19.07.2019 (Print) |
Published by: |
ISSAC '19 Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation
ISSAC '19 Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation
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Title of the series: | - |
Volume number: | - |
First publication: | Yes |
Version: | - |
Page: | pp. 155 - 162 |
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Keine Version vorhanden |
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ISBN (e-book): | - |
eISSN: | - |
DOI: | http://dx.doi.org/10.1145/3326229.3326239 |
Homepage: | - |
Open access |
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Publication date: | 19.07.2019 |
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ISSN: | - |
Homepage: | https://dl.acm.org/citation.cfm?doid=3326229.3326239 |
Authors
Elisabeth Gaar (internal) | ||||
Daniel Krenn (internal) | ||||
Susan Margulies
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Angelika Wiegele (internal) |
Assignment
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Fakultät für Technische Wissenschaften
Institut für Mathematik
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AT - 9020 Klagenfurt am Wörthersee |
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Research Cluster | No research Research Cluster selected |
Peer reviewed |
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working groups | No working group selected |
Cooperations
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Uppsala Universitet
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SE - 75105 Uppsala |
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United States Naval Academy, Department of Mathematics
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US Annapolis, MD |
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