We propose an univesal scheme to design loop-free and superstabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of...

Given a complete graph on n nodes with metric edge costs, the minimum-cost khop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest root-leaf-path in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(log n) times that of a minimum-cost k-hop spanning-tree.

We investigate multi-source spanning tree problems where, given a graph with edge weights and a subset of the nodes defined as sources, the object is to find a spanning tree of the graph that minimizes some distance related cost metric. This problem can be used to model multicasting in a network where messages are sent from a fixed collection of senders and communication takes place along the e...

The minimum degree spanning tree problem has been studied extensively. In this paper, we present a polynomial time algorithm for the minimum degree spanning tree problem on directed acyclic graphs. The algorithm starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree. We can prove the algorithm must reduce a vertex of the maximum degree for each ...

With applications in communication networks, the minimum stretch spanning tree problem is to find a T of graph G such that maximum distance between two adjacent vertices minimized. The has been proved NP-hard and fixed-parameter polynomial algorithms have obtained for some special families graphs. In this paper, we concentrate on optimality characterizations typical classes We determine exact f...

Given a set of nodes N (i 1, 2, ..., n) which may represent cities and a set of requirements ria which may represent the number of telephone calls between N and N j, the problem is to build a spanning tree connecting these n nodes such that the total cost of communication of the spanning tree is a minimum among all spanning trees. The cost of communication for a pair of nodes is r;a multiplied ...

In this paper we propose a limit characterization of the behaviour of classes of graphs with respect to their number of spanning trees. Let {Gn} be a sequence of graphs G0,G1,G2, . . . that belong to a particular class. We consider graphs of the form Kn −Gn that result from the complete graph Kn after removing a set of edges that span Gn. We study the spanning tree behaviour of the sequence {Kn...