Minimalizace odchozího stupně vrcholu v téměř pravidelném grafu

Abstract

This thesis is focused on the minimization of the maximum outdegree of vertex in an almost regular graph. The almost regular graph is a graph in which the difference between maximum and minimum degree of vertex is at most two. First we will show how to determine the optimal value of maximum outdegree of given almost regular graph and then we will show the way, how we can find the orientation with minimized maximum outdegree. We also give Matlab algorithm which finds optimal edge orientation for given almost regular graph. Our results can be used in parallel numerical computing where given object is divided into subdomains and each thread is used for computing on one subdomain and on some parts of the boundary of this subdomain. The edge orientation of a dual graph (each subdomain is represented by one vertex and there is an edge between two vertices if the subdomains represented by these vertices are neighboring) determines which thread will be used for computing on the boundary between any two vertices as we want to minimize the largest number of tasks on a thread.