A tree-based multicast algorithm for wormhole-routed torus networks, which makes use of multiple edge-disjoint spanning trees is presented. A technique for constructing two spanning trees in 2-dimensional torus networks is described. It is formally proven that this construction produces two edge-disjoint spanning trees in any 2-D torus network. Compared with an algorithm for construction of mul...

Some of the most efficient heuristics for the Euclidean Steiner minimal trees in the d-dimensional space, d ≥ 2, use Delaunay tessellations and minimum spanning trees to determine small subsets of geometrically close terminals. Their low-cost Steiner trees are determined and concatenated in a greedy fashion to obtain low cost trees spanning all terminals. The weakness of this approach is that o...

We revisit the minimal spanning tree problem in order to develop a theory of construction and counting of the minimal spanning trees in a network. The theory indicates that the construction of such trees consists of many di erent choices, all independent of each other. These results suggest a block approach to the construction of all minimal spanning trees in the network, and an algorithm to th...

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 ...

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.

We consider the problem of finding a spanning tree satisfying a family of additional constraints. Several settings have been considered previously, the most famous being the problem of finding a spanning tree with degree constraints. Since the problem is hard, the goal is typically to find a spanning tree that violates the constraints as little as possible. Iterative rounding has become the too...

In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set S ⊆ V(G) of cardinality n(k − 1) + c + 2, there exists a vertex set X ⊆ S of cardinality k such that the degree sum of vertices in X is at least |V(G)| − c − 1. Then G has a spanning tree T with maximum de...