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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a 2-approximation algorithm for the unweighted case has been proposed, and the best approximation ratio known for the weighted case is 3, which is the best known approximation ratio.
Abstract: The minimum cost-tree cover problem is to compute a minimum cost-tree T in a given connected graph G with costs on the edges, such that the vertices spanned by T form a vertex cover for G. The problem is supposed to occur in applications of vertex cover and in edge-dominating sets when additional connectivity is required for solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the 3-approximation algorithms for such cases are far from practical due to their inefficiency.In this article we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost-tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST); and, to determine which leaves to trim, it uses both the primal-dual schema and an instance layering technique adapted from the local ratio method.

9 citations

Journal Article
TL;DR: The algorithm is based on the low-cost shortest path tree algorithm DDSP and through improving on the search procedure, a Fast Low-cost Shortest Path Tree (FLSPT) algorithm is presented in this paper.
Abstract: Low-Cost Shortest Path Tree is a commonly-used multicast tree type, which can minimize the end-to-end delay and at the same time reduce the bandwidth requirement if possible. Based on the low-cost shortest path tree algorithm DDSP (destination-driven shortest path) and through improving on the search procedure, a Fast Low-cost Shortest Path Tree (FLSPT) algorithm is presented in this paper. The Shortest Path Tree constructed by the FLSPT algorithm is the same as that constructed by the DDSP algorithm, but its computation complexity is lower than that of the DDSP algorithm. The simulation results with random network models show that FLSPT algorithm is

9 citations

Journal ArticleDOI
TL;DR: It is shown that any spanning tree defined by the edges corresponding to a first visit of a vertex, appears with a probability proportional to its weight, which is the product of the weight of its edges.

9 citations

Journal ArticleDOI
TL;DR: A new GIS tool using most commonly known rudimentary algorithm called Prim’s algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network and helps to solve complex network MST problem easily, efficiently and effectively is developed.
Abstract: . minimum spanning tree (MST) of a connected, undirected and weighted network is a tree of that network consisting of all its nodes and the sum of weights of all its edges is minimum among all such possible spanning trees of the same network. In this study, we have developed a new GIS tool using most commonly known rudimentary algorithm called Prim’s algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network. This algorithm is based on the weight (adjacency) matrix of a weighted network and helps to solve complex network MST problem easily, efficiently and effectively. The selection of the appropriate algorithm is very essential otherwise it will be very hard to get an optimal result. In case of Road Transportation Network, it is very essential to find the optimal results by considering all the necessary points based on cost factor (time or distance). This paper is based on solving the Minimum Spanning Tree (MST) problem of a road network by finding it’s minimum span by considering all the important network junction point. GIS technology is usually used to solve the network related problems like the optimal path problem, travelling salesman problem, vehicle routing problems, location-allocation problems etc. Therefore, in this study we have developed a customized GIS tool using Python script in ArcGIS software for the solution of MST problem for a Road Transportation Network of Dehradun city by considering distance and time as the impedance (cost) factors. It has a number of advantages like the users do not need a greater knowledge of the subject as the tool is user-friendly and that allows to access information varied and adapted the needs of the users. This GIS tool for MST can be applied for a nationwide plan called Prime Minister Gram Sadak Yojana in India to provide optimal all weather road connectivity to unconnected villages (points). This tool is also useful for constructing highways or railways spanning several cities optimally or connecting all cities with minimum total road length.

9 citations

31 May 2012
TL;DR: Based on the results of research, Prim's algorithm computation time in finding the minimum spanning tree of a weighted graph will grow up along with increasing the number of points/vertices and thenumber of sides of the weighted graph.
Abstract: In this study, the algorithm used is Prim’s algorithm—an algorithm in graph theory to seek a minimum spanning tree for a weighted connected graph. The program used is a program created with Delphi 7 programming language used for searching the minimum spanning tree of a graph model with the weight of each form of distance/length connecting the points/vertices. Then display the information search process sequence of minimum spanning tree, the total number of minimum length and the resulting computing time to determine the efficiency of Prim’s algorithm. Based on the results of research, Prim's algorithm computation time in finding the minimum spanning tree of a weighted graph will grow up along with increasing the number of points/vertices and the number of sides of the weighted graph. Keywords:Prim’s Algorithm, Graph model, Minimum Spanning Tree

9 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
20224
202113
20208
201920
201815