中継効果の諸属性に関しての考察

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The initial weight of each vertices in transformed into a new weight by a monotonously increasing convex function in a network, when considering the shortest path problem to find out all of the shortest paths from one vertex to all the other vertices for the new weight. The graph given by the shortest path problem of this type is composed of a tree consisting of sub-paths (vertices) each of which are the shortest path between the vertices. The tree (the shortest path) changes according to types of the functions used for weight. For a sufficiently rapidly increasing function, we show that the tree consisting of the shortest paths agrees with the minimum spanning tree. The change of a tree by using a different convex function for weight is called a junction effect. We discuss the properties of the junction effect. By using a nonnegative real number for the weight, a numerical computer experiment is performed and its results are also presented.
岡山理科大学の論文
1989-03-20