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.

Phase unwrapping based on maximum cross-amplitude spanning tree algorithm: a comparative study

Abstract: A comparative study is made of the phase unwrapping algorithms that adopt either phase gradients or fringe amplitudes as a reliability measure in the selection of an unwrapping path. To compare with the minimum phase-gradient spanning tree algorithm, a maximum cross- amplitude spanning tree algorithm is proposed, which searches a spanning tree that maximizes overall edge weights given by the cross-amplitudes, i.e., the products of the fringe amplitudes of neighboring pixels. Noise-immunity of the cross-amplitude spanning tree algorithm is demonstrated by experiment and computer simulation.

Distributed computation of all node replacements of a minimum spanning tree

Abstract: In many network applications the computation takes place on the minimum-cost spanning tree (MST) of the network; unfortunately, a single link or node failure disconnects the tree. In this paper we consider for the first time the problem of computing all the replacement minimum-cost spanning trees distributively, and we efficiently solve the problem. We design a solution protocol and we prove that the total amount of data items communicated during the computation is O(n2). This communication can be achieved either transmitting O(n) long messages, if the system so allows, or O(n2) standard messages. Even in systems that do not allow long messages, the proposed protocol constitutes a significant improvement over the individual computation of the replacement trees.

Polylogarithmic Approximation for Minimum Communication Spanning Trees

Abstract: This paper considers a problem introduced in [Hu74], concerning the selection of a minimum communication spanning tree (MCT) for a given weighted network, namely, a tree that minimizes the total cost of transmitting a given set of communication requirements between n sites over the tree edges. Some special cases of the problem are solved in [Hu74]. An equivalent but slightly different formulation of the problem is given in [AKPW95], based on the concept of a spanning tree of low average stretch for weighted connected multigraphs. An algorithm is presented in [AKPW95] for constructing a spanning tree with average stretch O(2O{logn}) for any given multigraph, yielding an approximation algorithm for the MCT problem with a similar approximation ratio. It is conjectured in [AKPW95] that the true bound on average stretch is O(logn). This paper shows that for every weighted complete multigraph (with arbitrary multiplicities) there exists a spanning tree whose average stretch is bounded by O(ln n5/2 n?ln D), where D is the network''s diameter. The proof yields an approximation algorithm for minimum communication spanning trees with ratio O(ln5/2n?ln D).

Models and hybrid algorithms for inverse minimum spanning tree problem with stochastic edge weights

Abstract: An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the inverse minimum spanning tree problem with stochastic edge weights is investigated. The concept of -minimum spanning tree is initiated, and subsequently an -minimum spanning tree model and a probability maximization model are presented to formulate the problem according to different decision criteria. In order to solve the two stochastic models, hybrid genetic algorithms and hybrid simulated annealing algorithms are designed and illustrated by some computational experiments.