A linear-time algorithm for the minimum-ratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators. Disciplines Theory and Algorithms This article is available at Iowa State Univer...

Computing directed Minimum Spanning Tree (DMST) is a fundamental problem in graph theory. It applied wide spectrum of fields from computer network and communication protocol design to revenue maximization social networks syntactic parsing Natural Language Processing. State-of-the-art solutions are online algorithms that compute DMST for given root. For multi-query requirements, the algorithm in...

A number of minimum spanning tree algorithms have been proposed for lossy compression of image sets. In these algorithms, a complete graph is constructed from the entire image set and possibly an average image, and a minimum spanning tree is used to determine which difference images to encode. In this paper, we propose a hierarchical minimum spanning tree algorithm in which the minimum spanning...

Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More eecient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the po...