On the red/blue spanning tree problem

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...

On the Crossing Spanning Tree Problem

Given an undirected n-node graph and a set C of m cuts, the minimum crossing tree is a spanning tree which minimizes the maximum crossing of any cut in C, where the crossing of a cut is the number of edges in the intersection of this cut and the tree. This problem finds applications in fields as diverse as Computational Biology and IP Routing Table Minimization. We show that a greedy algorithm ...