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Evolutionary Algorithms in the Task of Boolean Satisfiability
Serédi, Silvester ; Vašíček, Zdeněk (referee) ; Sekanina, Lukáš (advisor)
The goal of this Master's Thesis is finding a SAT solving heuristic by the application of an evolutionary algorithm. This thesis surveys various approaches used in SAT solving and some variants of evolutionary algorithms that are relevant to this topic. Afterwards the implementation of a linear genetic programming system that searches for a suitable heuristic for SAT problem instances is described, together with the implementation of a custom SAT solver which expoloits the output of the genetic program. Finally, the achieved results are summarized.
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Circle packing and Möbius transformations
Porvichová, Janka ; Zeman, Peter (advisor) ; Kratochvíl, Jan (referee)
A graph can be represented by various geometric representations. In this work we focus on the circle packing representation. We state various concepts impor- tant for proving results regarding this kind of representation. We introduce a known proof of existence of a circle packing for planar graphs and a proof of existence of a primal-dual circle packing for 3-connected graphs. Next, we focus on computational complexity of extending the representation for a given partial circle packing. We examine the proof of the theorem stating that deciding whet- her such an extension exists is an NP-hard problem. We introduce our theoretical algorithm for extension construction based on real RAM machine. 1
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Implementation of operations in double-ended heaps
Bardiovský, Vojtech ; Koubek, Václav (advisor) ; Hubička, Jan (referee)
There are several approaches for creating double-ended heaps from the single-ended heaps. We build on one of them, the leaf correspondence heap, to create a generic double ended heap scheme called L-correspondence heap. This will broaden the class of eligible base single-ended heaps (e.g. by Fibonacci heap, Rank-pairing heap) and make the operations Decrease and Increase possible. We show this approach on specific examples for three different single-ended base heaps and give time complexity bounds for all operations. Another result is that for these three examples, the expected amortized time for Decrease and Increase operations in the L-correspondence heap is bounded by a constant.
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Evolutionary Algorithms in the Task of Boolean Satisfiability
Serédi, Silvester ; Vašíček, Zdeněk (referee) ; Sekanina, Lukáš (advisor)
The goal of this Master's Thesis is finding a SAT solving heuristic by the application of an evolutionary algorithm. This thesis surveys various approaches used in SAT solving and some variants of evolutionary algorithms that are relevant to this topic. Afterwards the implementation of a linear genetic programming system that searches for a suitable heuristic for SAT problem instances is described, together with the implementation of a custom SAT solver which expoloits the output of the genetic program. Finally, the achieved results are summarized.
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