Combinatorial Problems With Closure Structures
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We consider a specific class of combinatorial search respectively 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 structure can help to reduce time complexities. Moreover we propose two types of (structural) parameterizations of instance classes based on the closure property and outline how it could be used to achieve fixed-parameter tractability (FPT) characterizations. In this setting, three example problems are described: a covering problem from combinatorial geometry, a variant of the autarky problem in propositional logic, and a specific graph problem on finite forests.
KeywordsExact algorithmics Closure operator FPT Combinatorial optimization Computational complexity
- 3.Cook SA (1971) The complexity of theorem proving procedures. In: Proceedings of the 3rd ACM Symposium on Theory of Computing, ACM, Ohio, USA, pp 151–158Google Scholar
- 9.Porschen S (2005) On the rectangular subset closure of point sets. Proc ICCSA/CGA 2005, LNCS 3480:796–805Google Scholar
- 12.Porschen S (2009) An FPT-variant of the shadow problem with Kernelization. Proc ICCS 2009, 432–439, Hong KongGoogle Scholar
- 13.Porschen S (2011) On problems with closure properties. Lecture notes in engineering and computer science: Proc IMECS 2011, pp. 258–262, 16–18 March, 2011, Hong KongGoogle Scholar