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1. Combinatorial Optimization : Three Applications
Sammanfattning : Combinatorial optimization is a diverse area of mathematics. It concerns optimization on feasible regions defined by discrete sets, graphs, hypergraphs, matroids, etc. . . LÄS MER
2. On Some Combinatorial Optimization Problems : Algorithms and Complexity
Sammanfattning : This thesis is about the computational complexity of several classes of combinatorial optimization problems, all related to the constraint satisfaction problems.A constraint language consists of a domain and a set of relations on the domain. For each such language there is a constraint satisfaction problem (CSP). LÄS MER
3. Combinatorial Slice Theory
Sammanfattning : Slices are digraphs that can be composed together to form larger digraphs.In this thesis we introduce the foundations of a theory whose aim is to provide ways of defining and manipulating infinite families of combinatorial objects such as graphs, partial orders, logical equations etc. LÄS MER
4. Algorithmic Bounds for Presumably Hard Combinatorial Problems
Sammanfattning : In this thesis we present new worst case computational bounds on algorithms for some of the most well-known NP-complete and #P-complete problems and their optimization variants. We consider graph problems like Longest Path, Maximum Cut, Number of Perfect Matchings, Chromatic and Domatic Number, as well as Maximum k-Satisfiability and Set Cover. LÄS MER
5. Analysis of Algorithms for Combinatorial Auctions and Related Problems
Sammanfattning : The thesis consists of four papers on combinatorial auctions and a summary. The first part is more of a practical nature and contains two papers. In the first paper, we study the performance of a caching technique in an optimal algorithm for a multi-unit combinatorial auction. LÄS MER