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.

An Algorithm for the Minimum Spanning Tree Problem with Uncertain Structures

Abstract: The minimum spanning tree problem consists to find the smallest weight among all possible trees in a network. It is one of the main problems of graphs theory, since it has a wide range of applications in Engineering and Computation areas, such as: electricity distribution networks, information storage, transportation, etc. In this paper is proposed an exact algorithm to the minimum spanning tree problem with uncertain structures. It is based on the mainly papers of the literature and presents a solution ordered set of minimum spanning trees. The uncertainties of the structures are resolved using the fuzzy sets theory. The algorithm was tested on literature instances having the same results. Its complexity is O((v-a)(v^2)), where v is the node sets and a is the arcs sets.

Approximation algorithms for k-source bottleneck routing cost spanning tree problems - Extended abstracts

Abstract: In this paper, we investigate two spanning tree problems of graphs with k given sources Let G =( V, E, w) be an undirected graph with nonnegative edge lengths and S ⊂ V a set of k specified sources The first problem is the k-source bottleneck vertex routing cost spanning tree (k-BVRT) problem, in which we want to find a spanning tree T such that the maximum total distance from any vertex to all sources is minimized, ie, we want to minimize maxv∈V s∈S dT (s, v) ,i n which dT (s, v) is the length of the path between s and v on T The other problem is the k-source bottleneck source routing cost spanning tree (k-BSRT) problem, in which the objective function is the maximum total distance from any source to all vertices, ie, maxs∈S v∈V dT (s, v) In this paper, we present a polynomial time approximation scheme (PTAS) for the 2-BVRT problem For the 2-BSRT problem, we first give (2 + e)-approximation algorithm for any e> 0, and then present a PTAS for the case that the input graphs are restricted to metric graphs Finally we show that there is a simple 3-approximation algorithm for both the two problems with arbitrary k

Minimum Spanning Tree Clustering Algorithm

Abstract: The existing clustering algorithm can not discover clusters with arbitrary shape and multi-density using few parameters. In this paper we present a new clustering algorithm named MSTClust which is based on minimum spanning tree. The MSTClust can discover clusters with arbitrary shape and multi-density,can dispose multidimensional data,can detect outer point and have a good expansibility. In allusion to MSTClust we propose an objective function which refers to statistical Information of the weight of edges in minimum spanning tree. Finally the experimental result showed the effectiveness and efficiency of MSTClust and proved that the objective function have good astringency.

A heuristic algorithm for solving Steiner tree problem on urban traffic network

Abstract: The Steiner tree problem connects a subset of given nodes called terminals that this connection is absolutely a tree and it has the minimum cost. In this tree due to the reduction of cost of path, some non-terminal nodes are used, which called Steiner nodes. The Steiner tree problem has various usages that one of them is routing in the urban traffic networks. In such networks with a large amount of nodes and edges, finding the optimum path which connects small amounts of terminals is desired. Since these problems usually have wide scales, we should use heuristic algorithms, which find the near optimum Steiner tree in polynomial time. In this paper, a heuristic algorithm is proposed that needs O (n (m + n log n)). The algorithm finds the near optimum answer of Steiner tree on the given graph. The results of investigations show that this algorithm finds more accurate answers in comparison to the previous ones.