THE LOCATION OF CENTRAL STRUCTURES IN GRAPHS (NETWORKS, ABSOLUTE, PATH CENTER)
Abstract
The location of the center of a graph has traditionally been a point location study. In the spirit of recent work by Slater (1981) and Hedetniemi et. al. (1982), we seek to generalize the idea of central path location within the existing framework of point location studies. In conjunction with these path location problems, we introduce a new optimization problem--the subtree covering problem. This new problem is related to the central path location problem in the same way the point covering problems are related to the point center problems. A second aspect of our research is to consider central point location when the underlying graph is treelike. As a first step towards exploiting treelike structures, we develop algorithms which solve the absolute center problem on cactus graphs and "almost" Husimi trees. This technique--exploiting the underlying graph structure--shows great promise in providing a broader class of graphs on which point center location problems can be solved in polynomial time.
Degree
Ph.D.
Subject Area
Industrial engineering
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