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\Large
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{\Huge The Department of Computer Science\\ 
University of Nevada, Reno}

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{\Large cordially invites you to a Master's colloquium}

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        {\Large \bf Parallel Computation and Graphical Visualization \\
        of the Minimum Crossing Number of a Graph}
 

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        A thesis submitted in partial fulfillment of the\\
        requirements for the degree of Master of Science\\
        with a major in Computer Science.

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        by

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	Umid Tadjiev


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\noindent
        {\bf Abstract:} 
	Finding the minimum crossing number of a graph is an
	interesting and challenging problem in graph theory and applied
	mathematics.  Real world applications of this problem, such as
	circuit layout and network design, are becoming more and more
	important.
%
	This thesis presents a parallel algorithm for finding the
	minimum crossing number of a graph, based on the first
	sequential algorithm. % presented in \cite{hh96:apafctmcnoag}.
%	This parallel algorithm was tested on various architectures and
%	a comparison of the corresponding results is given, including
%	running time, efficiency, and speedup.  Implementation of the
%	algorithm gives us an ability to verify conjectures proposed
%	for various families of graphs, as well as apply the algorithm
%	to real world applications.

	Another important aspect of the problem is ability to draw the
	solution on the $2-D$ plane. This thesis also gives an overview
	of graph drawing algorithms, starting with the famous result by
	F\'{a}ry, and presents a new algorithm for drawing complete
	graphs, that uses the output of the previous algorithm.



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\Huge
{\bf 3:30 pm, Friday, May 15, 1998}
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{\bf Room 322D, Paul Laxalt Mineral Engineering}

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for more information contact \\
Dr. Fred Harris @ 784-6571 (fredh@cs.unr.edu)
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