Title: Parameterized Complexity Author: Ondřej Suchý Department: Department of Applied Mathematics Advisor: Prof. RNDr. Jan Kratochvíl, CSc. Advisor's e-mail address: honza@kam.mff.cuni.cz Abstract: This thesis deals with the parameterized complexity of NP-hard graph problems. We explore the complexity of the problems in various scenarios, with respect to miscellaneous parameters and their combina- tions. Our aim is rather to classify in this multivariate manner whether the particular parameters make the problem fixed-parameter tractable or intractable than to present the algorithm achieving the best running time. In the questions we study typically the first-choice parameter is unsuccessful, in which case we propose to use less standard ones. The first family of problems investigated provides a common general- ization of many well known and studied domination and independence problems. Here we suggest using the dual parameterization and show that, in contrast to the standard solution-size, it can confine the in- evitable combinatorial explosion. Further studied problems are ana- logues of the Steiner problem in directed graphs. Here the parameter- ization by the number of terminals to be connected seems to be previ- ously unexplored in the directed setting. Unfortunately, the problems are shown to be...
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:300399 |
| Date | January 2011 |
| Creators | Suchý, Ondřej |
| Contributors | Kratochvíl, Jan, Telle, Jan Arne, Obdržálek, Jan |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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