Computation of a Tree 3-Spanner on Trapezoid Graphs

TL;DR

This paper presents an efficient algorithm for computing a tree 3-spanner in trapezoid graphs, which are relevant in network design and distributed systems, improving the understanding of spanning structures in these graphs.

Contribution

The paper introduces the first polynomial-time algorithm for finding a tree 3-spanner specifically on trapezoid graphs, expanding the class of graphs with known spanning tree algorithms.

Findings

Algorithm runs in polynomial time proportional to the number of vertices.

Successfully constructs a tree 3-spanner for trapezoid graphs.

Enhances applications in network design and distributed computing.

Abstract

In a graph, a spanning tree is said to be a tree t-spanner of the graph if the distance between any two vertices in is at most times their distance in . The tree t-spanner has many applications in networks and distributed environments. In this paper, an algorithm is presented to find a tree -spanner on trapezoid graphs in time, where is the number of vertices of the graph.