Drawing a tree as a minimum spanning tree approximation

A 3-Approximation for the Minimum Tree Spanning k Vertices

In this paper we give a 3-approximationalgorithm for the problem ojJnding a minimum tree spanning any k-vertices in a graph. Our algorithm extends to a 3-approximation algorithm for the minimum tour that visits any k-vertices.

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 ...

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 Stock Market Filtering Model Based on Minimum Spanning Tree in Financial Networks

There have been several efforts in the literature to extract as much information as possible from the financial networks. Most of the research has been concerned about the hierarchical structures, clustering, topology and also the behavior of the market network; but not a notable work on the network filtration exists. This paper proposes a stock market filtering model using the correlation - ba...

A Probabilistic Minimum Spanning Tree Algorithm