Browsing by Author "Dr. Matthias Stallmann, Committee Chair"

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    Crossing Minimization in k-layer graphs
    (2009-01-06) Gupta, Saurabh; Dr. Carla D. Savage, Committee Member; Dr. Matthias Stallmann, Committee Chair; Dr. Rada Chirkova, Committee Member
    The crossing minimization problem in graphs has been extensively studied for the case when graphs are to be embedded on two layers. There are many well known heuristics for the 2-layer crossing minimization problem, like, for example, the barycenter and the median heuristic. The problem has not been studied much for k-layer graphs. The k-layer graph crossing minimization problem has specific application in aesthetic design of hierarchical structures, in VLSI circuit design to reduce the total wire length and crosstalk, and in various organization charts, flow diagrams and large graphs that arise in activity-based management. In our thesis work, we have extended the 2-layer graph heuristics to the crossing minimization problem for k-layer graphs. We have proposed twenty six heuristics for the k-layer graph problem. We have tested all the proposed heuristics on various classes of graphs instances including the structures that arise in activity-based management. The proposed heuristics have significantly outperformed the traditional sweep based heuristics. Additional experiments performed on the best performing heuristics have helped us to propose new enhancements on those heuristics, which have improved the performance of the heuristics further.
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    A New Heuristic for the Hamiltonian Circuit Problem
    (2008-12-22) Narayanasamy, Prabhu; Dr. Carla Savage, Committee Member; Dr. Matthias Stallmann, Committee Chair; Dr. James Lester, Committee Member
    In this research work, we have discussed a new heuristic for the Hamiltonian circuit problem. Our heuristic initially builds a small cycle in the given graph and incrementally expands the cycle by adding shorter cycles to it. We added features to our base heuristic to deal with the problems encountered during preliminary experiments. Most of our efforts were directed at cubic Cayley graphs but we also considered random, knight tour and geometric graphs. Our experimental results were mixed. In some but not all cases the enhancements improved performance. Runtime of our heuristic was generally not competitive with existing heuristics but this may be due to inefficient implementation. However, our experiments against geometric graphs were very successful and the performance was better than the Hertel’s SCHA algorithm, even in terms of runtime.