Optimization realization of a distance matrix †

†This research was completely supported by Deapartment of Computer Science and Engineering, School of Engineering, Shiraz University Shiraz, Iran.

Abstract

In this paper we present an algorithm for optimum realization of n × n distance matrix by a weighted digraph. The method has two major steps. In the first step the index pairs of the nonzero finite elements of the given matrix are partitioned such that the elements corresponding to each class have the same value. The second step involves a systematic graph construction process that uses the information from the first step and an algorithm for computing a distance matrix for a digraph. We have proved the correctness of our algorithm and shown that the optimum realization is unique. An example is presented for illustrating the algorithm.

Keywords:

• Distance matrix
• digraph
• optimum realization

C.R. Categories:

• 3.24
• 5.32

†This research was completely supported by Deapartment of Computer Science and Engineering, School of Engineering, Shiraz University Shiraz, Iran.

†This research was completely supported by Deapartment of Computer Science and Engineering, School of Engineering, Shiraz University Shiraz, Iran.

Notes

†This research was completely supported by Deapartment of Computer Science and Engineering, School of Engineering, Shiraz University Shiraz, Iran.