Minimum spanning trees in networks with varying edge weights

Hutson, Kevin R.; Shier, Douglas R.

doi:10.1007/s10479-006-0043-6

Cited by 17 publications

(19 citation statements)

References 18 publications

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“…To study the efficiency of the proposed algorithms, we have conducted three set of simulation experiments on four well-known stochastic benchmark graphs borrowed from [41,42]. The first set of experiments aims to investigate the relationship between the learning rate of Algorithm 1 and the error rate in standard sampling method.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In [41], Hutson and Shier studied several approaches to find (or to optimize) the minimum spanning tree when the edges undergo the weight changes. Repeated Prim method, cut-set method, cycle tracing method, and multiple edge sensitivity method are the proposed approaches to find the MST of the stochastic graph in which the edge weight can assume a finite number of distinct values as a random variable.…”

Section: Introductionmentioning

confidence: 99%

“…Computer simulation shows that Algorithm 5 outperforms the others in terms of sampling rate (the number of samples) and convergence rate. To investigate the efficiency of the best proposed algorithm (Algorithm 5), we compare Algorithm 5 with MESM proposed by Hutson and Shier [41]. The obtained results show that Algorithm 5 is superior to MESM in terms of running time and sampling rate.…”

Section: Introductionmentioning

confidence: 99%

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Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Torkestani

Meybodi

2011

Applied Soft Computing

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Due to the hardness of solving the minimum spanning tree (MST) problem in stochastic environments, the stochastic MST (SMST) problem has not received the attention it merits, specifically when the probability distribution function (PDF) of the edge weight is not a priori known. In this paper, we first propose a learning automata-based sampling algorithm (Algorithm 1) to solve the MST problem in stochastic graphs where the PDF of the edge weight is assumed to be unknown. At each stage of the proposed algorithm, a set of learning automata is randomly activated and determines the graph edges that must be sampled in that stage. As the proposed algorithm proceeds, the sampling process focuses on the spanning tree with the minimum expected weight. Therefore, the proposed sampling method is capable of decreasing the rate of unnecessary samplings and shortening the time required for finding the SMST. The convergence of this algorithm is theoretically proved and it is shown that by a proper choice of the learning rate the spanning tree with the minimum expected weight can be found with a probability close enough to unity. Numerical results show that Algorithm 1 outperforms the standard sampling method. Selecting a proper learning rate is the most challenging issue in learning automata theory by which a good trade off can be achieved between the cost and efficiency of algorithm. To improve the efficiency (i.e., the convergence speed and convergence rate) of Algorithm 1, we also propose four methods to adjust the learning rate in Algorithm 1 and the resultant algorithms are called as Algorithm 2 through Algorithm 5. In these algorithms, the probabilistic distribution parameters of the edge weight are taken into consideration for adjusting the learning rate. Simulation experiments show the superiority of Algorithm 5 over the others. To show the efficiency of Algorithm 5, its results are compared with those of the multiple edge sensitivity method (MESM). The obtained results show that Algorithm 5 performs better than MESM both in terms of the running time and sampling rate.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Torkestani

Meybodi

2011

Applied Soft Computing

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“…The first group is concerned with investigating the efficiency of the proposed algorithms on three stochastic graphs borrowed from Ref. 49 and shown in Figs. 8, 9, and 10, and the second group of the simulation evaluates the scalability of the proposed algorithms on dense stochastic graphs.…”

Section: Resultsmentioning

confidence: 99%

Learning Automata-Based Algorithms for Finding Minimum Weakly Connected Dominating Set in Stochastic Graphs

Torkestani

Meybodi

2010

Int. J. Unc. Fuzz. Knowl. Based Syst.

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A weakly connected dominating set (WCDS) of graph G is a subset of G so that the vertex set of the given subset and all vertices with at least one endpoint in the subset induce a connected sub-graph of G. The minimum WCDS (MWCDS) problem is known to be NP-hard, and several approximation algorithms have been proposed for solving MWCDS in deterministic graphs. However, to the best of our knowledge no work has been done on finding the WCDS in stochastic graphs. In this paper, a definition of the MWCDS problem in a stochastic graph is first presented and then several learning automata-based algorithms are proposed for solving the stochastic MWCDS problem where the probability distribution function of the weight associated with the graph vertices is unknown. The proposed algorithms significantly reduce the number of samples needs to be taken from the vertices of the stochastic graph. It is shown that by a proper choice of the parameters of the proposed algorithms, the probability of finding the MWCDS is as close to unity as possible. Experimental results show the major superiority of the proposed algorithms over the standard sampling method in terms of the sampling rate.

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“…As earlier mentioned, the aim of an absolute MST algorithm is to find minimum spanning trees from graphs, assuming fixed weights of edges (Hutson and Shier, 2006). Although stochastic minimum spanning tree (SMST) algorithm concerns with graphic edges the weights of which are a stochastic variable, most scenarios assume edges weights are fixed (Ishii et al, 1981;Dhamdhere et al, 2005).…”

Section: Stochastic Minimum Spanning Tree Problemmentioning

confidence: 99%

A learning automata-based algorithm using stochastic minimum spanning tree for improving life time in wireless sensor networks

Asgari¹,

Torkashvand²,

Barati³

2013

Int. J. Phys. Sci.

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Several algorithms have already been provided for problems of data aggregation in wireless sensor networks, which somehow tried to increase networks lifetimes. In this study, we dealt with this problem using a more efficient method by taking parameters such as the distance between two sensors into account. In this paper, we presented a heuristic algorithm based on distributed learning automata with variable actions set for solving data aggregation problems within stochastic graphs where the weights of edges change with time. To aggregate data, the algorithm, in fact, creates a stochastic minimum spanning tree (SMST) in networks where variable distances of links are considered as edges, and sends data in the form of a single packet to central node after data was processed inside networks. To understand this subject better, we modeled the problem for a stochastic graph having edges with changing weights. Although this assumption that edges weights change with time makes our task difficult, the results of simulations indicate relatively optimal performance of this method.

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Minimum spanning trees in networks with varying edge weights

Cited by 17 publications

References 18 publications

Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Learning Automata-Based Algorithms for Finding Minimum Weakly Connected Dominating Set in Stochastic Graphs

A learning automata-based algorithm using stochastic minimum spanning tree for improving life time in wireless sensor networks

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