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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11 Aug 2006
TL;DR: This paper shows how the tree contraction method can be applied to compute the cardinality of the minimum vertex cover of a two-terminal series-parallel graph and shows that in the new computational environment, a parallel algorithm is superior to the best possible sequential algorithm, in terms of the accuracy of the solution computed.
Abstract: In this paper we show how the tree contraction method can be applied to compute the cardinality of the minimum vertex cover of a two-terminal series-parallel graph. We then construct a real-time paradigm for this problem and show that in the new computational environment, a parallel algorithm is superior to the best possible sequential algorithm, in terms of the accuracy of the solution computed. Specifically, there are cases in which the solution produced by a parallel algorithm that uses p processors is better than the output of any sequential algorithm for the same problem, by a factor superlinear in p.
3 citations
04 Jul 2012
TL;DR: The algorithm for determining how many vertices should be installed in a certain period in such a way so that the cost of installation is minimum is discussed.
Abstract: Given one center already set, The Multi Period Degree Constrained Minimum Spanning Tree Problem (MPDCMST) is a problem of determining how many vertices (can be computers, cities, and so on) should be installed in a certain period in such a way so that the cost of installation is minimum. After all the periods done, all of the vertices must be in the network, and still the cost of installation must be the minimum. In addition, the network itself has a degree restriction in every vertex which limits the number of links that incident to. In this paper we will discuss the algorithm we have developed and give results on 600 random table data. Keywords: multi period, degree constrained, minimum spanning tree
3 citations
01 Jan 2017
TL;DR: This paper claims to propose a unique solution to the problem of all possible spanning tree enumeration for a simple, symmetric, and connected graph based on the algorithmic paradigm named divide-and-conquer.
Abstract: This paper claims to propose a unique solution to the problem of all possible spanning tree enumeration for a simple, symmetric, and connected graph. It is based on the algorithmic paradigm named divide-and-conquer. Our algorithm proposes to perform no duplicate tree comparison and a minimum number of circuit testing, consuming reasonable time and space.
3 citations
TL;DR: In this article, the authors considered a special case of the generalized minimum spanning tree problem, where the vertex set is partitioned into clusters, and non-negative costs are associated with the edges.
Abstract: This paper is concerned with a special case of the Generalized Minimum Spanning Tree Problem. The Generalized Minimum Spanning Tree Problem is de¯ned on an undirected graph, where the vertex set is partitioned into clusters, and non-negative costs are associated with the edges. The problem is to ¯nd a tree of minimum cost containing exactly one vertex in each cluster. We consider a geometric case of the problem where the graph is complete, all vertices are situated in the plane, and Euclidean distance de¯nes the edge cost. We prove that the problem admits PTAS if restricted to grid clustering.
3 citations
TL;DR: A polynomial time algorithm for solving the minimum vertex ranking spanning tree problem on outerplanar graphs and it is proposed that this problem is NP-hard.
Abstract: The minimum vertex ranking spanning tree problem is to find a spanning tree of G whose vertex ranking is minimum. This problem is NP-hard and no polynomial time algorithm for solving it is known for non-trivial classes of graphs other than the class of interval graphs. This paper proposes a polynomial time algorithm for solving the minimum vertex ranking spanning tree problem on outerplanar graphs.
3 citations