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.

Stochastic Bottleneck Spanning Tree Problem on a Fuzzy Network

Abstract: This paper considers a fuzzy network version of the stochastic bottleneck spanning tree problem. Existence of each edge is not necessary certain and it is given by a certain value between 0 and 1. 1 means that it exists certainly and 0 means it does not exist. For intermediate numbers, a higher value corresponds to a higher possibility of existence. Furthermore each edge has a random cost independent to other edges. The probability that the maximum burden among these selected edges is not greater than the capacity should be not less than the fixed probability. Under the above setting, we seek a spanning tree minimizing the capacity and maximizing the minimal existence possibility among these selected edges. Since usually there is no spanning tree optimizing two objectives at a time, we derive an efficient solution procedure to obtain a set of some non-dominated spanning tree after defining non-domination of spanning trees. Finally we discuss the further research problems.

The minimum spanning tree and duality in graphs

Abstract: Several algorithms for the minimum spanning tree are known. The Blue-red algorithm is a generic algorithm in this field. A new proof for this algorithm is presented, based upon the duality of circuits and cuts in a graph. The Blue-red algorithm is genetic, because the other algorithms can be regarded as special instances. This is shown using the same duality.

Penentuan pohon rentang minimum berdasarkan kondisi geografis suatu wilayah dengan algoritma prim

Abstract: Determination of the minimum spanning tree are widely used to solve optimization problems of finding solutions to problems that require minmum. In the electricity distribution network, minimum spanning tree (MST) is used to find the minimum length of cable for electricity network system becomes more optimal. Minimum weight of a MST primary distribution power network is strongly influenced by the geographical conditions of a region in the form of contour data. This research was done by designing a model of primary distribution power network graph in accordance with the data obtained. In finding the minimum weight for each side of the network graph should include parameters elevation, high point / node, and the distance between points / nodes. Furthermore, the graph is done by computer calculation and simulation to get the electricity distribution network primary MST using Prim's algorithm with the help of ArcView GIS 3.3 program through the avenue script. Prim's algorithm included in the category of good or efficient algorithms, because the shape of polynomial time complexity in n, where n is a measure of the number of vertices or sides. Based on the test results have shown that the algorithm Prim MST ability to determine the primary distribution grid is much better if based on the geographical conditions of a region. In addition, Prim's algorithm graph computation time in generating the MST based on the data that is not based on the contour and contour data are quadratic. Keywords: minimum spanning tree, prim's algorithm, contours, complexity time

An Improved MPH-Based Delay-Constrained Steiner Tree Algorithm

Abstract: In order to optimize cost and decrease complexity with a delay upper bound, the delay-constrained Steiner tree problem is addressed. Base on the new delay-constrained MPH (DCMPH_1) algorithm and through improving on the select path, an improved MPH-based delay-constrained Steiner tree algorithm is presented in this paper. With the new algorithm a destination node can join the existing multicast tree by selecting the path whose cost is the least; if the path’s delay destroys the delay upper bound, the least-cost path which meets the delay upper bound can be constructed through the least-cost path, and then is used to take the place of the least-cost path to join the current multicast tree. By the way, a low-cost multicast spanning tree can be constructed and the delay upper bound isn’t destroyed. Experimental results through simulations show that the new algorithm is superior to DCMPH_1 algorithm in the performance of spanning tree and the space complexity.

Minimum vertex ranking spanning tree problem for chordal and proper interval graphs

Abstract: A vertex k-ranking of a simple graph is a coloring of its ver- tices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et. al. proved in (Np-hardness proof and an approximation algorithm for the minimum vertex ranking span- ning tree problem, Discrete Appl. Math. 154 (2006) 2402-2410) that the decision problem: given a simple graph G, decide whether there exists a spanning tree T of G such that T has a vertex 4-ranking, is NP- complete. In this paper we improve this result by proving NP-hardness of finding for a given chordal graph its spanning tree having v ertex 3- ranking. This bound is the best possible. On the other hand we prove that MVRST problem can be solved in linear time for proper interval graphs.