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.

A Robust, Responsive, Distributed Tree-Based Routing Algorithm Guaranteeing N Valid Links per Node in Wireless Ad-Hoc Networks

Abstract: In this paper, we present two new tree growing algorithms. The pairing algorithm allows for the local approximate implementation of global algorithms such as Prim's or Dijkstra 's algorithm. A node requires only information from its neighborhood acquired by local message exchange. Any global cost function that can be locally calculated can be used with this algorithm. The N-SafeLinks Algorithm establishes look-up tables with N possible links per node. Implementing an additional constraint it is guaranteed that each link leads to the sink, ruling out the possibility of loops. Therefore, if maximal N-l links per node are broken there is still a guaranteed connection to the destination node (sink) for every node. A proof of this property is presented. As demonstrated in simulations the trees are close to optimum. The algorithms can be utilized for static routing in wireless single-sink Ad-Hoc networks with safety critical applications where timeliness, robustness and energy efficiency is crucial.

A Vertex Oriented Approach to Minimum Cost Spanning Tree Problems

Abstract: In this paper we consider spanning tree problems, where n players want to be connected to a source as cheap as possible. We introduce and analyze (n!) vertex oriented construct and charge procedures for such spanning tree situations leading in n steps to a minimum cost spanning tree and a cost sharing where each player pays the edge which he chooses in the procedure. The main result of the paper is that the average of the n! cost sharings provided by our procedure is equal to the P-value for minimum cost spanning tree situations introduced and characterized by Branzei et al. (2004). As a side product, we find a new method, the vertex oriented procedure, to construct minimum cost spanning trees.

DNA algorithm for minimum vertex cover problem based on molecular computation

Abstract: The minimum vertex cover problem is to find a minimum subset of vertex which covers all the edges in a given graph. This is a NP-complete problem. The DNA algorithm for the vertex cover problem based on bio-molecular technology is introduced. The key of the algorithm is that mathematical problem is mapped onto DNA strand and the vertex is coded by DNA sequence. The problem is solved by tube operation that performs the basic core processing and extraction that makes the results visible. On the basis of the experiment method of bio-molecular, the algorithm is an effective method. Finally, the advantage and disadvantage are discussed, the future research directions are pointed out.

Augmenting the edge-connectivity of a spider tree

Abstract: Given an undirected, 2-edge-connected, and real weighted graph G, with n vertices and m edges, and given a spanning tree T of G, the 2-edge-connectivity augmentation problem with respect to G and T consists of finding a minimum-weight set of edges of G whose addition to T makes it 2-edge-connected While the general problem is NP-hard, in this paper we prove that it becomes polynomial time solvable if T can be rooted in such a way that a prescribed topological condition with respect to G is satisfied In such a case, we provide an ${\mathcal O}(n(m+h+\delta^{3}))$ time algorithm for solving the problem, where h and δ are the height and the maximum degree of T, respectively A faster version of our algorithm can be used for 2-edge connecting a spider tree, that is a tree with at most one vertex of degree greater than two This finds application in strengthening the reliability of optical networks.

A fast algorithm for data exchange in reconfigurable tree structures

Abstract: The paper presents a fast algorithm for data exchange in a network of processors organized as a reconfigurable tree structure. For a given data exchange table, the algorithm generates a sequence of tree configurations in which the data exchanges are to be executed. A significant feature of the algorithm is that each exchange is executed in a tree configuration in which the source and destination nodes are adjacent to each other. It has been proved in a theorem that for every pair of nodes in the reconfigurable tree structure, there always exist two and only two configurations in which these two nodes are adjacent to each other. The algorithm utilizes this fact and determines the solution so as to optimize both the number of configurations required and the time to perform the data exchanges. Analysis of the algorithm shows that it has linear lime complexity, and provides a large reduction in run-time as compared to an existing algorithm. This is well confirmed from the experimental results obtained by executing a large number of randomly generated data exchange tables. Another significant feature of the algorithm is that the bit size of the routing information code is always two bits, irrespective of the number of nodes in the tree. This not only increases the speed of the algorithm but also results in simpler hardware inside each node. >