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.

Overlay Multicast Tree Minimizing Average Time Delay

Abstract: In this work, we present an overlay multicast tree constructing algorithm to minimize the average time delay from the sender to end-systems. At the same time, the proposed algorithm considers the computing power and the network condition of each end-system as a control variable and thus we can avoid the disastrous case that loads are concentrated to only several end-systems. The multicast tree is constructed by clustering technique and modified Dijkstra’s algorithm in two steps, i.e. tree among proxy-senders and tree in each cluster. By the experimental results, we show that the proposed algorithm can provide an effective solution.

The Application of Minimum Spanning Tree Algorithm in the Water Supply Network

Abstract: The system of urban water supply network is the important lifeline project of the city. With the continuous development of social economy, people are no longer satisfied with water supply requirements, but to put forward higher requirements for the safety, reliability and economy of the water supply. Based on actual demands to solve the economic problems of water supply network to ensure the lowest costs in the laying the pipelines. First, establishing a mathematical model of water supply network, so we can use the knowledge of graph theory to solve this problem; from the above that, the minimum spanning tree was needed to establish to ensure that costs are the lowest in the case of pipeline connectivity. Then using the Kruskal algorithm to generate minimum spanning tree; finally, an example was analyzed to verify its practicality, and the algorithm solved the problem of water supply network in laying pipelines successfully. Introduction Water is the source of life, and is closely related to human survival. Water supply network is a water distribution system created by people, which is a vital part of water supply system. Water supply system in the order usually consists of water intake structures, water treatment structures, water supply pumping stations, adjustment structures, drainage pipes and water supply pipe network. The water supply network mainly refers to the urban water supply pipe network system, which is an important material base to protect the city people's life and develop production and construction [1]. Urban water supply pipe network system can be regarded as an important lifeline of urban engineering. The traditional view is that the water supply network's mission is to provide sufficient amount of water, the residents have enough water to use. However, with the continuous development of social economy, people put forward higher requirements for the safety, reliability and economy of the water supply. Specifically, in the process of water supply, the quality of supplied water is healthy or not, such as water pipe corrosion or other factors lead to water quality problems; after an earthquake or major disaster, the water supply network is reliable or not, urban water supply network can be normal without the occurrence of secondary disasters; pipe network not only to have above two characteristics, economic issues is the focus. In the case of the entire water supply network connectivity, we must to ensure the lowest costs that aim to produce hedge-fund-like returns at lower cost. So in recent years, research on the economic aspect of water supply network is increasingly attracted people's attention. Water supply system is an important infrastructure of the city, and it also is an important part of urban lifeline project, which plays an irreplaceable role in protecting economic development, ensuring social production and meeting human life [2]. The Establishment of the Mathematical Model for Water Supply Network In laying city network, the street interchanges must be considered because the pipelines must along the street to lay. In case of that water supply network can connect all users to make it with the lowest costs. To achieve this goal, you must consider how to select and handle these interchanges. This problem is a serious problem. The solution of this problem can provide a standard for the International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) © 2015. The authors Published by Atlantis Press 52 laying of water supply network to ensure best design effect. According to graph theory, the water supply network can be viewed as a graph. So the contents of the water supply network need to be translated into the language of graph theory to help solve the problem of water supply network costs. The language from pipelines to graph is described as follows [3]: a) The water supply center and users in the planning area are referred to as nodes, the intersection of the street known as the intersections. The nodes and intersections are regarded as the vertices of graph. So the issue can be converted to the shortest path between each vertex, and each vertex must be connected indirectly or not indirectly. b) The routes that may be laying between nodes and intersections can be considered as edges of the graph. c) The sum of construction costs and operating costs of each line is regarded as the weights of edges. The sum of weights is the minimum that is the lowest costs, that is the purpose of the design you want to achieve. Through the above three steps, the water supply network can form a graph, this graph includes the vertices, edges and weights. Using G (V, E, W) to represent, V represents the set of vertices in the graph; E represents the set of edges in the graph; W represents the set of weights of each edge in the graph. Setting T is a spanning tree of diagram of G, then: W(T)=∑ Wuv euv∈T (1) Among them, W(T) is the sum of weights in the tree of T; euv is the any edge in the tree of T; Wuv is the weights of euv. The purpose of design is to require the minimum values of W(T). Only this way can ensure the lowest costs of laying pipelines. In summary, the problem of the minimum costs of the water supply network may be as a problem of seeking minimum spanning tree in the graph. The minimum spanning tree must exist. According to the actual situation, each node will certainly connected when laying water supply network, so there will be a minimum spanning tree certainly. There are a variety of algorithms to generate minimum spanning tree, such as Prim algorithm, Kruskal algorithm and simple algorithm and so on [4]. The Basic Concept of Algorithm Kruskal algorithm chooses the right edge according to the ascending order of weights to construct a minimum spanning tree. Kruskal algorithm, also known as avoidance circle method, starting from the shortest side, the edge attached to the tree does not form a loop, then the edge can be added to the tree, otherwise examine the next edge [5]. Specific steps are as follows: (1) Firstly, all vertices in connectivity network need to be added to minimum spanning tree to Start Arranging according to the ascending order of weights Setting d(vj)=min{d(u), d(v)}

Multi-routing method for full ant group algorithm based on distance

Abstract: The present invention discloses a multicast routing method based on a distance complete ant colony algorithm. Firstly, a distance complete graph is established for a multicast routing network; then multicast trees are constructed randomly based on the ant colony algorithm and a Prim algorithm, wherein, the setting of heuristic information makes the algorithm to be more disposed to select target nodes. A redundant detection and a correction are carried out on the generated multicast trees and the updating of local information elements is implemented. Lastly, after all of the ants accomplish the constitution of a solution, the updating of the entire information elements is implemented, the information elements on the side of the most preferable tree in history are reinforced. By simulating the test result and the comparison with the algorithms of the same type, it shows that the distance complete ant colony algorithm of the present invention is capable of solving the problem of multicast routing more quickly.

Penerapan algoritma greedy dalam menentukan minimum spanning trees pada optimisasi jaringan listrik jala

Abstract: This article discusses the applied of greedy algorithm principle in finding the optimum solution in determine minimum spanning tree on graph. Graph theory is one of the studies in discrete mathematics that are widely applied in various scope. This article is a literature study and applied of nets electricity network optimization using Prims algorithm and Kruskal algorithm. Network Nets System is one type of electrical network system construction. Based on results of the study and discussion can be concluded that the application of greedy algorithm using Prims algorithm and Kruskal algorithm in determine minimum spanning tree on its principle is the same. However, after a comparison between the two algorithms we consider that the ideal algorithm used to optimize the nets electric network is the Kruskal algorithm because in the case of the electric network has few sides and many vertices.

Optimal Cost-Sensitive Distributed Minimum Spanning Tree Algorithm

Abstract: In a network of asynchronous processors, the cost to send a message can differ significantly from one communication link to another. Assume that associated with each link is a positive weight representing the cost of sending one message along the link and the cost of an algorithm executed on a weighted network is the sum of the costs of all messages sent during its execution. We present a distributed Minimum Cost Spanning tree algorithm that is optimal with respect to this cost measure.