Algorithms of Fast Search of Center, Radius and Diameter on Weighted Graphs

TL;DR

This paper introduces fast algorithms for computing the radius, diameter, and centers of weighted graphs, efficiently using only a small subset of vertices, and compares their performance to existing methods.

Contribution

It presents novel algorithms that efficiently find metric characteristics of weighted graphs by utilizing only a small fraction of vertices, improving computational speed.

Findings

Algorithms outperform traditional methods on various inputs

Significant reduction in computation time achieved

Effective in large-scale weighted graphs

Abstract

Two problems in the search of metric characteristics on weighted undirected graphs with non-negative edge weights are being considered. The first problem: a weighted undirected graph with non-negative edge weight is given. The radius, diameter and at least one center and one pair of peripheral vertices of the graph are to be found. In the second problem we have additionally calculated the distances matrix. For the problems being considered, we proposed fast search algorithms which use only small fraction of graph's vertices for the search of the metric characteristics. The proposed algorithms have been compared to other popular methods of solving problems considered on various inputs.