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 Efficient Algorithm for Minimum Vertex Cover Problem

Abstract: An efficient parallel algorithm for solving the minimum vertex cover problem using binary neural network is presented. The proposed algorithm which is designed to find the smallest vertex cover of a graph, uses the binary neural network to get a near-smallest vertex cover of the graph, and adjusts the balance between the constraint term and the cost term of the energy function to help the network escape from the state of the near-smallest vertex cover to the state of the smallest vertex cover or better one. The proposed algorithm is tested on a large number of random graphs and benchmark graphs. The simulation results show that the proposed algorithm is very satisfactory and better than previous works for solving the minimum vertex cover problem.

The Iterative Minimum Cost Spanning Tree Problem

Abstract: The minimum cost spanning tree problem consists in constructing a network of minimum cost that connects all agents to the source and distributes the cost among the agents in a fair way. We develop a framework for the iterative minimum cost spanning tree problem. In the iterative setting, agents arrive over time and desire to be connected to a source in different rounds in order to receive a service from the source. We provide an algorithm for the iterative minimum cost spanning tree problem in order to connect the agents from the different rounds to the source in a minimal way. Moreover, we discuss the complexity of the algorithm. To divide the cost of the constructed network among the agents in a fair way we propose different charge rules. One class of charge rules is defined in such a way that the inefficiency of the network, caused by agents joining in different rounds, is equally divided among the agents who use the network. A second class of charge rules charges the incoming agents as much as possible such that previously connected agents can be reimbursed. However, we want to avoid that agents are better off by construction their own network. Furthermore, we prove that the charge rules satisfy several properties. This provides the basis for comparing the charge rules and allows for assessment of their fairness in a particular situation.

A complete spanning tree maintenance algorithm and its complexity

Abstract: The spanning tree maintenance problem for an LAN model in which node processors may halt and recover is considered. An algorithm meeting the conditions that the spanning tree is an L-ary complete tree and that nodes halt or recover singly is presented. The message complexity of this algorithm is shown to be comparable with local computational complexity