<p>In this thesis we study problems related to approximation of asymmetric TSP. First we give worst case examples for the famous algorithm due to Frieze, Gabiati and Maffioli for asymmetric TSP with triangle inequality. Some steps in the algorithm consist of arbitrary choices. To prove lower bounds, these choices need to be specified. We show a worst case performance with some deterministic assumptions on the algorithm and then prove an expected worst case performance for a randomised version of the algorithm. The algorithm by Frieze et al. produces a spanning cactus and makes a TSP tour by shortcuts. We have proven that determining if there is a spanning cactus in a general asymmetric graph is an NP-complete problem and that finding a minimum spanning cactus in a complete, directed graph with triangle inequality is equivalent to finding the TSP tour and the problems are equally hard to approximate. We also give three other results; we show a connection between asymmetric TSP and TSP in a bipartite graph, we show that it is NP-hard to find a cycle cover in a bipartite graph without cycles of length six or less and finally we present some results for a new problem with ordered points on the circle.</p>

In this thesis we study problems related to approximation of asymmetric TSP. First we give worst case examples for the famous algorithm due to Frieze, Gabiati and Maffioli for asymmetric TSP with triangle inequality. Some steps in the algorithm consist of arbitrary choices. To prove lower bounds, these choices need to be specified. We show a worst case performance with some deterministic assumptions on the algorithm and then prove an expected worst case performance for a randomised version of the algorithm. The algorithm by Frieze et al. produces a spanning cactus and makes a TSP tour by shortcuts. We have proven that determining if there is a spanning cactus in a general asymmetric graph is an NP-complete problem and that finding a minimum spanning cactus in a complete, directed graph with triangle inequality is equivalent to finding the TSP tour and the problems are equally hard to approximate. We also give three other results; we show a connection between asymmetric TSP and TSP in a bipartite graph, we show that it is NP-hard to find a cycle cover in a bipartite graph without cycles of length six or less and finally we present some results for a new problem with ordered points on the circle. / QC 20101122

The aim of this diplomma thesis is to build a platform of the phenomenon of emergence in complex information systems. To our best knowledge, there has not been provided any similar concept in either internetional or domestic academic literature. The necessity to create a concept of the phenomenon of emergence in the enviroment of information systems stems from the observation of the fragmented knowledge about the emergence concept in the pool of scientific papers where the link between emergence and information systems is missing. As a result, the platform created in this work is the reaction to the lack of the above mentioned link, while the ambition is to provide a cornerstone for potential emergence's utilization in information systems. In this work, we provide a construct that describes and analyzes the characteristics, technics and methodologies in connection with the phenomenon of emergence, placing a great deal on the specifics of the emergence in complex information sytems. Special attention is paid to eNetworks that we consider to be the best enviroment for examining the characteristics of emergent behavior in regards to the concept of complexity. This enviroment shows suitable conditions for the analysis of information spreading and dynamic interactions, which is primarily connected with generating of emergent characteristic. In order to understand the causality of specific emergence's demonstrations, we take a closer look at two approaches: Holonistic multi-agemt systems and iterative simulation process.