Minimum Spanning Trees and Types of Dissimilarities

Geometric Minimum Spanning Trees

Let S be a set of n points in < d. We present an algorithm that uses the well-separated pair decomposition and computes the minimum spanning tree of S under any Lp or polyhedral metric. It has an expected running time of O(n logn) for uniform distributions. Experimentalresults show that this approachis practical. Under a variety of input distributions, the resultingimplementation is robust and ...

Minimum Spanning Trees∗

1 Background Members of some secret party want to shutdown some high risk communication channals, while preserving low risk channals to ensure that members are still connected in the secret network.

Minimum Spanning Trees

Let G =< V,E > be a connected graph with real-valued edge weights: w : E → R, having n vertices and m edges. A spanning tree in G is an acyclic subgraph of G that includes every vertex of G and is connected; every spanning tree has exactly n− 1 edges. A minimum spanning tree (MST) is a spanning tree of minimum weight which is defined to be the sum of the weights of all its edges. Our problem is...

Geometri Minimum Spanning Trees

Low-Degree Minimum Spanning Trees

Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the Lp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where the maximum degree is minimized. We give the best-known bounds for the maximum MST degree for ar...