Showing papers on "Prim's algorithm published in 1985"

On the History of the Minimum Spanning Tree Problem

Abstract: It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of Kruskal(1956) and Prim (1957) as the sources of the problem and its first efficient solutions, despite the citation by both of Boruvka (1926) as a predecessor. In fact, there are several apparently independent sources and algorithmic solutions of the problem. They have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century. We shall explore and compare these works and their motivations, and relate them to the most recent advances on the minimum spanning tree problem.

An algorithm for distributed computation of a spanningtree in an extended LAN

Abstract: A protocol and algorithm are given in which bridges in an extended Local Area Network of arbitrary topology compute, in a distributed fashion, an acyclic spanning subset of the networkThe algorithm converges in time proportional to the diameter of the extended LAN, and requires a very small amount of memory per bridge, and communications bandwidth per LAN, independent of the total number of bridges or the total number of links in the networkAlgorhymeI think that I shall never see A graph more lovely than a treeA tree whose crucial property Is loop-free connectivityA tree which must be sure to span So packets can reach every LANFirst the Root must be selected By ID it is electedLeast cost paths from Root are traced In the tree these paths are placedA mesh is made by folks like me Then bridges find a spanning tree

A Note on Finding Minimum-Cost Edge-Disjoint Spanning Trees

Abstract: Let G be an undirected graph with n vertices and m edges, such that each edge has a real-valued cost. We consider the problem of finding a set of k edge-disjoint spanning trees in G of minimum total edge cost. This problem can be solved in polynomial time by the matroid greedy algorithm. We present an implementation of this algorithm that runs in O(m log m + k2n2) time. If all edge costs are the same, the algorithm runs in O(k2n2) time. The algorithm can also be extended to find the largest k such that k edge-disjoint spanning trees exist in O(m2) time. We mention several applications of the algorithm.

An almost linear time and O(nlogn+e) Messages distributed algorithm for minimum-weight spanning trees

Abstract: A distributed algorithm is presented that constructs the minimum-weight spanning tree of an undirected connected graph with distinct edge weights and distinct node identities. Initially each node knows only the weight of each of its adjacent edges. When the algorithm terminates, each node knows which of its adjacent edges are edges of the tree. For a graph with n nodes and e edges, the total number of messages required by our algorithm is at most 5nlogn+2e, and each message contains at most one edge weight or one node identity plus 3+logn bits. Although our algorithm has the same message complexity as the previously known algorithm by Gallager et al., the time complexity of our algorithm takes at most O(nG(n))+ time units, an improvement from Gallager's O(nlogn)+. A worst case O(nG(n)) is also possible.