On the Minimum Density Interconnection Tree Problem

Minimum Density Interconnection Trees

IYe discuss a new minimum density objectave for spanning and Steaner tree constructaons. This formu-latzoii is motzvated b y the need for balanced usage of routang resources t o achaeve iiztnzmum-area VLSI layouts. We present eficient heunstzcs for constructnng low-density spaniazng trees, and prove that their outputs are on average wafhzn small constants of optimal with respeci to both tree we...

On the Minimum Label Spanning Tree Problem

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 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.

The Minimum Guarding Tree Problem

Given a set L of non-parallel lines in the plane and a nonempty subset L′ ⊆ L, a guarding tree for L′ is a tree contained in the union of the lines in L such that if a mobile guard (agent) runs on the edges of the tree, all lines in L′ are visited by the guard. Similarly, given a connected arrangement S of line segments in the plane and a nonempty subset S ′ ⊆ S, we define a guarding tree for S...