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.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: This paper considers the case of finding the lowest cost replacement edge for each edge of the minimum spanning tree and finds it in linear time, since the most vital edge is the tree edge whose removal causes the highest cost.
Abstract: Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a replacement edge for each edge in the MST. For example, when a traffic accident closes a road in a transportation network, or a line goes down in a communication network, the replacement edge may reconnect the MST at lowest cost. In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes $O(m \alpha(m, n))$ time, where $\alpha(m, n)$ is the inverse Ackermann's function. Given the MST and sorted non-tree edges, our algorithm is the first that runs in $O(m+n)$ time and $O(m+n)$ space to find all replacement edges. Moreover, it is easy to implement and our experimental study demonstrates fast performance on several types of graphs. Additionally, since the most vital edge is the tree edge whose removal causes the highest cost, our algorithm finds it in linear time.
TL;DR: This paper suggests an Hybrid MST algorithm which consists of the merits of both Borůvka's 1 st stage and Kruskal M ST algorithm, which can be used as the generalized MST algorithms.
Abstract: In this paper, to obtain the Minimum Spanning Tree (MST) from the graph with several nodes having the same weight, I applied both Borůvka and Kruskal MST algorithms. The result came out to such a way that Kruskal MST algorithm succeeded to obtain MST, but not did the Prim MST algorithm. It is also found that an algorithm that chooses Inter-MSF MWE in the 2 nd stage of Borůvka is quite complicating. The 1 st stage of Borůvka has an advantage of obtaining Minimum Spanning Forest (MSF) with the least number of the edges, and on the other hand, Kruskal MST algorithm has an advantage of always obtaining MST though it deals with all the edges. Therefore, this paper suggests an Hybrid MST algorithm which consists of the merits of both Borůvka's 1 st stage and Kruskal MST algorithm. When applied additionally to 6 graphs, Hybrid MST algorithm has a same effect as that of Kruskal MST algorithm. Also, comparing the algorithm performance speed and capacity, Hybrid MST algorithm has shown the greatest performance Therefore, the suggested algorithm can be used as the generalized MST algorithm.Keywords:Minimum Spanning Tree, Undirected, Distinct Weights, Same Weights, Cycle
01 Oct 2005
TL;DR: A hybrid evolution strategy on RSTP based upon the Prim algorithm was presented and the computational results show that the evolution strategy is better than the previously proposed other heuristic.
Abstract: The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. A hybrid evolution strategy on RSTP based upon the Prim algorithm was presented. The computational results show that the evolution strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolution strategy is about 11%, which is almost similar to that of optimal solutions.
TL;DR: In this paper, a direct and elementary method for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before is provided.
Abstract: A direct and elementary method is provided in this paper for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before.
16 Dec 2006
TL;DR: This paper presents a polynomial time algorithm for the minimum degree spanning tree problem on directed acyclic graphs, and can prove the algorithm must reduce a vertex of the maximum degree for each phase, and finally result in an optimal tree.
Abstract: The minimum degree spanning tree problem has been studied extensively. In this paper, we present a polynomial time algorithm for the minimum degree spanning tree problem on directed acyclic graphs. The algorithm starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree. We can prove the algorithm must reduce a vertex of the maximum degree for each phase, and finally result in an optimal tree. The algorithm terminates in O(mnlogn) time, where m and n are the number of edges and vertices respectively.