On the SPANNING k-TREE problem

The (K, k)-Capacitated Spanning Tree Problem

This paper considers a generalization of the capacitated spanning tree, in which some of the nodes have capacity K, and the others have capacity k < K. We prove that the problem can be approximated within a constant factor, and present better approximations when k is 1 or 2.

On the Minimum Label Spanning Tree Problem

On the Minimum Diameter Spanning Tree Problem

We point out a relation between the minimum diameter spanning tree of a graph and its absolute 1-center. We use this relation to solve the diameter problem and an extension of it eeciently.

On the Red/Blue Spanning Tree Problem

A geometric spanning tree of a point set S is a tree whose vertex set is S and whose edge set is a set of non-crossing straight line segments with endpoints in S. Given a set of red points and a set of blue points in the plane, the red/blue spanning tree problem is to find a geometric spanning tree for red points and a geometric spanning tree for blue points such that the number of crossing poi...

On the Euclidean Minimum Spanning Tree Problem∗

Given a weighted graph G(V,E), a minimum spanning tree for G can be obtained in linear time using a randomized algorithm or nearly linear time using a deterministic algorithm. Given n points in the plane, we can construct a graph with these points as nodes and an edge between every pair of nodes. The weight on any edge is the Euclidean distance between the two points. Finding a minimum spanning...