We present a general framework for obtaining efficient algorithms for computing minimum spanning trees. We use this framework to derive the classical algorithms of Prim, Kruskal and Bor̊uvka. We then describe the randomized linear-time algorithm of Karger, Klein and Tarjan. The algorithm of Karger, Klein and Tarjan uses deterministic linear-time implementations of a verification algorithm of Kom...

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 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...

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 ...

We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞ E(Ln) = ζ(3) and show that E(Ln) = ζ(3) + c1 n + c2+o(1) n4/3 where c1, c2 are explicitly defined constants.

still of wide interest, not only in the analysis of remotely sensed images. We describe a new approach to the extraction of networks of narrow curvilinear features such as road and river networks from remotely sensed MINIMUM COST PATHS images. The approach begins with the identification of points in the image with a high probability of being on the network. In the second stage the broad topolog...

We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satis...es cost monotonicity. We also give characterization theorems for the new rule as well as the much-studied Bird allocation. We show that the principal di¤erence between these two rules is in terms of their consistency properties. JEL Classi...cation Numbers: D7

This work provides a practical method for the development of rural road networks in rural areas of developing countries. The proposed methodology enables to determine obligatory points in the rural road network maximizing the number of settlements that have access to basic services within a given maximum distance. The proposed methodology is simple and practical, hence, highly applicable to rea...

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...