A central problem in wide area networks is to eeciently multicast a message to all members (hosts) of a target group. One of the most eeective methods to multicast a message is to send the message along the edges of a spanning tree connecting all the members of the group. In this paper we propose a new fully distributed algorithm to build a minimum spanning tree (MST) in a generic communication...

This paper describes the application of a dynamic programming approach to find minimum flow cost spanning trees on a network with general nonlinear arc costs. Thus, this problem is an extension of the Minimum Spanning Tree (MST) problem since we also consider flows that must be routed in order to satisfy user needs. In fact, the MST, usually, considers fixed arc costs and in our case the arc co...

We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the relatively developed Guangdong Province is lower than others, with significant industrial...

We consider the problem of preprocessing an edgeweighted tree in order to quickly answer queries of the following type: does a given edge belong in the minimum spanning tree of ? Whereas the offline minimum spanning tree verification problem admits a lovely linear time solution, we demonstrate an inherent inverseAckermann type tradeoff in the online MST verification problem. In particular, any ...

We consider the problem of preprocessing an edgeweighted tree T in order to quickly answer queries of the following type: does a given edge e belong in the minimum spanning tree of T [ feg? Whereas the offline minimum spanning tree verification problem admits a lovely linear time solution, we demonstrate an inherent inverseAckermann type tradeoff in the online MST verification problem. In parti...

In a complete graph with independent uniform (or exponential) edge weights, let be the minimum-weight spanning tree (MST), and MST after deleting edges of all previous trees. We show that each tree's weight converges in probability to constant , we conjecture . The problem is distinct from Frieze Johansson's minimum combined k edge-disjoint trees; indeed, With an w “arriving” at time Kruskal's ...

Koml os has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a linear-time algorithm for verifying a minimum spanning tree. Our algorithm combines the result of Koml os with a preprocessing and...

The minimum spanning tree (MST) is a combinatorial optimization problem: given a connected graph with a real weight ("cost") on each edge, find the spanning tree that minimizes the sum of the total cost of the occupied edges. We consider the random MST, in which the edge costs are (quenched) independent random variables. There is a strongly disordered spin-glass model due to Newman and Stein [P...

An O(n log n) heuristic for the Euclidean Steiner Minimal Tree (ESMT) problem is presented. The algorithm is based on a decomposition approach which first partitions the vertex set into triangles via the Delaunay triangulation, then "recomposes" the suboptimal Steiner Minimal Tree (SMT) according to the Voronoi diagram and Minimum Spanning Tree (MST) of the point set. The ESMT algorithm was imp...