Topic
Prim's algorithm
About: Prim's algorithm is a research topic. Over the lifetime, 775 publications have been published within this topic receiving 17971 citations. The topic is also known as: DJP algorithm & Jarník algorithm.
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DOI•
01 Mar 1997TL;DR: This work proposes a linear time algorithm for computing a cheap vertex failure tolerant graph, given the Delaunay triangulation, which bounds the cost of the minimum spanning multi-tree.
Abstract: The concept of the minimum spanning tree (MST) plays an important role in topological network design, because it models a cheapest connected network. In a tree, however, the failure of a vertex can disconnect the network. In order to tolerate such a failure, we generalize the MST to the concept of a cheapest biconnected network. For a set of points in the Euclidean plane, we show that it is NP-hard to find a cheapest biconnected spanning graph, where edge costs are the Euclidean distances of the respective points. We propose a different type of subgraph, based on forbidding (due to failure) the use of a vertex. A minimum spanning multi-tree is a spanning graph that contains for each possible forbidden vertex a spanning tree that is minimum among the spanning trees that do not use the forbidden vertex. We propose a worst-case time optimal algorithm for computing a minimum spanning multi-tree for a planar Euclidean point set. A minimum spanning multi-tree is cheap, even though it embeds a linear number of MSTs: Its cost is more than the MST cost only by a constant factor. Furthermore, we propose a linear time algorithm for computing a cheap vertex failure tolerant graph, given the Delaunay triangulation. This graph bounds the cost of the minimum spanning multi-tree from above.
5 citations
TL;DR: This work proposes a solution to the problem of creating minimum spanning tree (MST) in cognitive radio network, a message passing based distributed algorithm that is useful for data dissemination in Cognitive Radio Networks.
5 citations
TL;DR: An O(nlogn) time algorithm is developed, which improves the previously best result of O(nlog^2n) by using centroid decomposition, and the time complexity is optimal in the algebraic computation tree model.
5 citations
01 Mar 1987
TL;DR: A distributed algorithm for constructing a spanning tree for connected undirected graphs where nodes correspond to processors and edges correspond to two-way channels and maxid is the maximal processor identity.
Abstract: We present a distributed algorithm for constructing a spanning tree for connected undirected graphs. Nodes correspond to processors and edges correspond to two-way channels. Each processor has initially a distinct identity and all processors perform the same algorithm. Computation as well as communication is asynchronous. The total number of messages sent during a construction of a spanning tree is at most 2E+3NlogN. The maximal message size is loglogN+log(maxid)+3, where maxid is the maximal processor identity.
5 citations
Journal Article•
TL;DR: The idea of the improved Kruskal algorithm is deleting the edge which has the maximum weight and does not influence diagram connectivity when deleted it, until there are number of n-1 edges.
Abstract: In the application of Kruskal algorithm to get the minimum spanning tree,the time of selecting edge at least was n-1.When the number of side m and vertex n satisfy the relationship m≤2n-2,Kruskal algorithm can be improved.When the number of selecting edge time was at most n-1,the improved algorithm was used to get the solution.The idea of the improved algorithm is deleting the edge which has the maximum weight and does not influence diagram connectivity when deleted it,till there are number of n-1 edges.The time of improved algorithm is reduced by theory.
5 citations