Pruning a minimum spanning tree

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., ...

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 ...

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...

A Probabilistic Minimum Spanning Tree Algorithm

Derivation of a Minimum Spanning Tree Algorithm