Construction of Multiplicative Graph Spanners using Minimum Connected Dominating Set with Bounded Diameter

Abstract

A Multiplicative Spanner is a spanning sub-graph $H(V, E^{\prime})$ of a graph $G(V, E)$ such that $distance(u, v, H) where $distance(u, v, G)$ is the shortest distance between the vertices $u$ and $v$ in $G$ . The parameter $t$ is called the multiplicative stretch of the spanner. When the size of the graph is reduced to construct a spanner, the shortest distance between the vertices increases, consequently the stretch factor also increases. It is known that the construction of spanners with optimum size-stretch is hard. Many researchers proposed efficient algorithms that yield proven near optimal results. In this paper we propose a quadratic time algorithm to construct multiplicative t-spanners with a bound on the stretch factor.