Algorithm 42. Enclosure of a point to the minimum spanning tree

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...

A Probabilistic Minimum Spanning Tree Algorithm

The Filter-Kruskal Minimum Spanning Tree Algorithm

We present Filter-Kruskal – a simple modification of Kruskal’s algorithm that avoids sorting edges that are “obviously” not in the MST. For arbitrary graphs with random edge weights, Filter-Kruskal runs in time O ( m + n log n log m n ) , i.e. in linear time for not too sparse graphs. Experiments indicate that the algorithm has very good practical performance over the entire range of edge densi...