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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Heuristics for Length Bounded Cuts
 Madaj, Pavel ; Kolman, Petr (advisor) ; Koutecký, Martin (referee)
This thesis deals with the problem of finding a minimum length-bounded cut in a graph. We first provide a brief overview of the problem and its applications. We then discuss the known theoretical results and approximation algorithms. We look at the existing linear programming formulations and propose a new one. A concise discussion on potential hard instances, utilized for testing our formulations, is also incorporated. The focus of our analysis is on the performance and behavior of our proposed linear programming family, contrasting it with the established natural formulation. We also compare the performance of various heuristics and approximation algorithms in practice by examining their behaviour on a large set of small instances. 1
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Vertex-transitive Supergraphs
 Madaj, Pavel ; Tancer, Martin (advisor) ; Hušek, Radek (referee)
In this thesis we explore ways to extend graphs to supergraphs that are vertex-transitive. We introduce a template system for their construction. This system is used to provide a construction of vertex-transitive supergraphs of exponential size for general graphs and of quadratic size for bipartite graphs. For general graphs we also provide a quadratic lower bound. We also sketch an approach that could lead to bridging the time complexity gap between the graph isomorphism problem and the problem of recognizing vertex-transitive graphs. 1
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