A Characterization of Minimum Spanning Tree-Like Metric Spaces

4 Minimum Spanning Tree

This first algorithm is quite simple. (Though this was probably known earlier, its proof can be found in Prof. Indyk’s 1999 paper “Sublinear Time Algorithms for Metric Space Problems”.) Let Dij denote the distance between a pair of points i and j, over m total points. The entries of Dij must satisfy the triangle inequality; additionally the matrix is symmetric. Note that the matrix size (i.e., ...

On the Structure of Metric-like Spaces

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

A Metaheuristic Algorithm for the Minimum Routing Cost Spanning Tree Problem

The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start ...

Derivation of a Minimum Spanning Tree Algorithm

Parallel Minimum Spanning Tree Algorithm

The Minimal Spanning Tree (MST) problem is a classical graph problem which has many applications in various areas. In this paper we discuss a concurrent MST algorithm derived from Prim’s algorithm presented by Setia et al. in 2009, targeting symmetric multiprocessing (SMP) with a shared address space. The pseudocode of the algorithm is presented, combined with three interesting heuristics in or...