On Problems With Closure Properties

We consider a specific class of combinatorial search or optimization problems where the search space gives rise to a closure operator and essentially the hulls are the only relevant subsets that must be checked in a brute force approach. We suggest that such a closure property can help to reduce tim...

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Bibliographic Details
Published inWorld Congress on Engineering 2012. July 4-6, 2012. London, UK Vol. 2188; pp. 258 - 262
Main Author Porschen, Stefan
Format Journal Article
LanguageEnglish
Published 01.03.2010
Subjects
Closures
Combinatorial analysis
Hulls
Hulls (structures)
Mathematical analysis
Parametrization
Searching
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Summary:We consider a specific class of combinatorial search or optimization problems where the search space gives rise to a closure operator and essentially the hulls are the only relevant subsets that must be checked in a brute force approach. We suggest that such a closure property can help to reduce time complexities. Moreover we propose two types of (structural) parameterization of instance classes based on the closure property and outline how it could be used to achieve FPT characterizations. In this setting, three example problems are considered: a covering problem from combinatorial geometry, a variant of the autarky problem in propositional logic, and a specific graph problem on finite forests.
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ISSN:2078-0958