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.

Associative parallel algorithm for dynamic update of a minimum spanning tree after addition of a new node to a graph

Abstract: This paper proposes a new associative parallel algorithm for dynamic update of a minimum spanning tree after addition of a new node with all its incident edges to a graph. This algorithm is represented as the InsertVert procedure implemented on a model of an associative parallel system of the SIMD type with vertical processing (a STAR machine). The correctness of the procedure is proved and its time complexity is estimated.

Different time installation effect on the quality of the solution for the multiperiod installation problem using modified prim’s algorithm

Abstract: Most in network design problems, The Minimum Spanning Tree (MST) is usually used as the backbone. If we add degree restriction on its vertices (can represent cities, stations, etc) of the graph (represents the network), the problem becomes the Degree Constrained Minimum Spanning Tree (DCMST) problem. However, to do the installation or connecting the network, it is possible that the process must be done into some stages or periods. That situation occurs because of the weather constraint, fund constraint, etc. By restricting and dividing the stages or periods of the network’s installation, the problem emerges as The Multi Period Degree Constrained Minimum Spanning Tree (MPDCMST) problem or Multiperiod Installation Problem. We develop two algorithms based on Modified Prim’s algorithms (WAC1 and WAC2) to solve the MPDCMST problem, show and compare the different time installation effect on quality of the solution by implementing and comparing those algorithms using 300 generate problems. Keywords and phrases minimum spanning tree; degree constrained; installation, period

How to Trim an MST : A 2-Approximation Algorithm for Minimum Cost Tree Cover

Abstract: The minimum cost tree cover problem is to compute a minimum cost tree T in a given connected graph G with costs on the edges, such that the vertices of T form a vertex cover for G. The problem is supposed to arise in applications of vertex cover and edge dominating set when connectivity is additionally required in solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the known 3-approximation algorithm for such case is far from practical in its efficiency. In this paper we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST), and to determine which leaves to trim, it uses both of the primal-dual schema and the local ratio technique in an interlaced fashion.

Binary identification problems for weighted trees

Abstract: The Binary Identification Problem for weighted trees asks for the minimum cost strategy (decision tree) for identifying a node in an edge weighted tree via testing edges. Each edge has assigned a different cost, to be paid for testing it. Testing an edge e reveals in which component of T - e lies the vertex to be identified. We give a complete characterization of the computational complexity of this problem with respect to both tree diameter and degree. In particular, we show that it is strongly NP-hard to compute a minimum cost decision tree for weighted trees of diameter at least 6, and for trees having degree three or more. For trees of diameter five or less, we give a polynomial time algorithm. Moreover, for the degree 2 case, we significantly improve the straightforward O(n3) dynamic programming approach, and provide an O(n2) time algorithm. Finally, this work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn.

A new hybrid evolutionary algorithm for the k-cardinality tree problem

Abstract: In recent years it has been shown that an intelligent combination of metaheuristics with other optimization techniques can significantly improve over the application of a pure metaheuristic. In this paper, we combine the evolutionary computation paradigm with dynamic programming for the application to the NP-hard k-cardinality tree problem. Given an undirected graph G with node and edge weights, this problem consists of finding a tree in G with exactly k edges such that the sum of the weights is minimal. The genetic operators of our algorithm are based on an existing dynamic programming algorithm from the literature for finding optimal subtrees in a given tree. The simulation results show that our algorithm is able to improve the best known results for benchmark problems from the literature in 60 cases.