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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TL;DR: An improved genetic algorithm to search the minimum spanning trees is given and can get a set of the solutions with higher probability in a shorter time.
Abstract: Based on the graphic theory and improved genetic algorithm,an improved genetic algorithm to search the minimum spanning trees is given . The algorithm uses binary code to represent the problem of minimum spanning trees. It designs the corresponding fitness function,operator and few controlling strategies to improve its speed and evolutionary efficiency.Only one solution can be gotten with running traditional al-gorithem atone time.The new algorithm can get a set of the solutions with higher probability in a shorter time.The experiment shows that it has a better performance than traditional methods.
TL;DR: It is shown that this problem of drawing a tree on parallel lines is solvable in time linear on the size of the tree, by presenting an algorithm which solves it recursively.
Abstract: We consider a problem of drawing a tree on parallel lines. In this problem we given a tree and an infinite number of parallel lines in the plane. The object is to draw the tree so that 1. (i) each vertex is placed on one of the given parallel lines, 2. (ii) no two edges intersect, and 3. (iii) the ‘height’ of each vertex is nondecreasing, while minimizing the total number of lines used. We show that this problem is solvable in time linear on the size of the tree, by presenting an algorithm which solves it recursively.
TL;DR: A fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property, and reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.
Abstract: This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge per vertex . Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.
01 Jan 2014
TL;DR: An algorithm base on firefly algorithm is suggested for solving the issue of minimum Steiner tree and the results of tests show that suggested algorithm compare to reported methods as genetic algorithm & ant colony enjoys more proficiency.
Abstract: The issue of finding minimum Steiner tree in a valuable graph is finding a tree by least cost on graph which involves special loop naming terminal. This issue is out of NP-Complete issues, therefore, several approximate algorithms as genetic algorithm, ant colony, learning automata &etc has reported. In this paper an algorithm base on firefly algorithm is suggested for solving the issue of minimum Steiner tree. The results of tests show that suggested algorithm compare to reported methods as genetic algorithm & ant colony enjoys more proficiency.