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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13 Oct 2011
TL;DR: A new approach of applying, conducting implementation experiments and analyzing some aspects of using ant algorithm for MRCT problem is introduced.
Abstract: Minimum routing cost spanning tree problem-MRCT is one of classical problems in network designing. In this paper, we will introduce a new approach of applying, conducting implementation experiments and analyzing some aspects of using ant algorithm for MRCT problem.
5 citations
TL;DR: The present algorithm implements Prim's procedure for calculating a minimum spanning tree in an undirected network when the edge costs can be scaled to integers in a moderate range and has been used to calculate minimum spanning trees for networks with up to 500 vertices and 24,000 edges.
Abstract: The problem of determining a minimum spanning tree arises in a number of application areas, including network reliability, pattern recognition, clustering, and design of distribution systems. The present algorithm implements Prim's procedure [7] for calculating a minimum spanning tree in an undirected network when the edge costs can be scaled to integers in a moderate range. While other codes for implementing Prim's procedure have been published [4, 6, 8, 9], all have used a two-dimensional array for storing the edge costs. As a result, such implementations have been limited to fairly small networks (e.g., 100 or fewer vertices). Moreover, these previous codes do not take advantage of network sparsity to reduce the computational effort. In contrast, the present code does exploit network sparsity and has been used to calculate minimum spanning trees for networks with up to 500 vertices and 24,000 edges. Even such large problems required less than 0.7 seconds of CPU time on an IBM 370/3033 computer (IBM Extended H FORTRAN compiler). For the algorithm given here, the edge costs are assumed to be positive integers with maximum edge cost CMAX. The network, assumed to be connected with NV vertices, is represented in forward star form [2, 3]. That is, for each vertex i E {1 . . . . . NV}, EPT( i ) is a pointer to the first position in a list E L I S T where the vertices j adjacent to i are stored consecutively. A list ECOST, of the same size as ELIST, stores the corresponding edge costs c(i, j) for the edges (i, j). It
5 citations
01 Sep 2012
TL;DR: A new genetic algorithm based on spanning tree-based encoding for the well-known MAX CUT problem is proposed and could obtain performance improvement on sparse graphs, which appear in real-world applications such as social networks and systems biology.
Abstract: Most of previous genetic algorithms for solving graph problems have used vertex-based encoding. In this paper, we introduce spanning tree-based encoding instead of vertex-based encoding for the well-known MAX CUT problem. We propose a new genetic algorithm based on this new type of encoding. We conducted experiments on benchmark graphs and could obtain performance improvement on sparse graphs, which appear in real-world applications such as social networks and systems biology, when the proposed methods are compared with ones using vertex-based encoding.
5 citations
Patent•
08 Jun 2016
TL;DR: In this paper, a Dijkstra algorithm was used to acquire a shortest path graph and calculate an influence coefficient of each branch according to the shortest-path graph of two end points of a branch.
Abstract: The invention relates to an offshore wind plant submarine cable wiring acquisition method. The method comprises the following steps of according to an electrical connection graph of an offshore wind plant, acquiring an adjacent matrix among nodes of the offshore wind plant and using the adjacent matrix to express a topology mode in the electrical connection graph and a branch weight among the modes; according to a Dijkstra algorithm, acquiring a shortest path graph and calculating an influence coefficient of each branch according to the shortest path graph of two end points of each branch; multiplying the branch weight in the adjacent matrix by the corresponding influence coefficient so as to acquire the weight of the branch and form a new adjacent matrix; for the acquired new adjacent matrix, using a Prim algorithm and taking a summit of a tree as a lead so as to acquire a minimum spanning tree W; according to a direct current trend equation, calculating a current value of each cable, selecting a submarine cable model so that a current-carrying capacity parameter of the submarine cable is greater than a calculated current value, determining a parameter value of each segment of the submarine cable and calculating submarine cable investment cost of the minimum spanning tree.
5 citations
TL;DR: A new parallel algorithm for updating the minimum spanning tree of an n -vertex graph following the addition of a new vertex is presented, superior to previous algorithms on this model that either obtain O(log n ) time performance using O( n 2 ) processors, or employ O(n ) processors but have a time complexity of O( log 2 n ).
5 citations