Heuristic algorithms for the triangulation of graphs

Cano, Andrés; Moral, Serafı́n

doi:10.1007/bfb0035941

Cited by 31 publications

(23 citation statements)

References 12 publications

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“…In [8] another particular heuristics based on the same idea arise, but attempting to avoid its weak points. The main underlying idea of these heuristics is that in the moment of deleting a variable it should be sought to minimise the corresponding 9 S(C i ).…”

Section: Groups or Clusters C I ∈ P(v )mentioning

confidence: 99%

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A Review on Distinct Methods and Approaches to Perform Triangulation for Bayesian Networks

Flores

Gámez

2007

Advances in Probabilistic Graphical Models

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Summary. Triangulation of a Bayesian network (BN) is somehow a necessary step in order to perform inference in a more efficient way, either if we use a secondary structure as the join tree (JT) or implicitly when we try to use other direct techniques on the network. If we focus on the first procedure, the goodness of the triangulation will affect on the simplicity of the join tree and therefore on a quicker and easier inference process.The task of obtaining an optimal triangulation (in terms of producing the minimum number of triangulation links a.k.a. fill-ins) has been proved as an NP-hard problem. That is why many methods of distinct nature have been used with the purpose of getting as good as possible triangulations for any given network, especially important for big structures, that is, with a large number of variables and links.In this chapter, we attempt to introduce the problem of triangulation, locating it in the compilation process and showing first its relevance for inference, and consequently for working with Bayesian networks. After this introduction, the most popular and used strategies to cope with the triangulation problem are reviewed, grouped into two main categories: heuristics and stochastic algorithms. Finally, another family of techniques could be understood as those based in decomposing the problem.

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Section: Groups or Clusters C I ∈ P(v )mentioning

confidence: 99%

“…Among the several heuristics that Cano and Moral [8] propose in their work, we find this approach called H2. This is very similar to minimum weight, at each case it chooses the variable X i , among all the possible variables to be deleted, which minimises S(i)/|Ω(X i )|.…”

Section: Groups or Clusters C I ∈ P(v )mentioning

confidence: 99%

A Review on Distinct Methods and Approaches to Perform Triangulation for Bayesian Networks

Flores

Gámez

2007

Advances in Probabilistic Graphical Models

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“…However, obtaining an optimum graph triangulation is known to be NP-hard [18]. For this purpose several advanced heuristic algorithms have been developed to aid the approximation of a good triangulation [19]. In our implementation we use the simple minimum degree heuristic to obtain an elimination ordering of the set of vertices V .…”

Section: A Chordal Graphsmentioning

confidence: 99%

Consistency of Chordal RCC-8 Networks

Sioutis

Koubarakis

2012

2012 IEEE 24th International Conference on Tools With Artificial Intelligence

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Abstract-We consider chordal RCC-8 networks and show that we can check their consistency by enforcing partial path consistency with weak composition. We prove this by using the fact that RCC-8 networks with relations from the maximal tractable subsetsĤ8, C8, and Q8 of RCC-8 have the patchwork property. The use of partial path consistency has important practical consequences that we demonstrate with the implementation of the new reasoner PyRCC8 , which is developed by extending the state of the art reasoner PyRCC8. Given an RCC-8 network with only tractable RCC-8 relations, we show that it can be solved very efficiently with PyRCC8 by making its underlying constraint graph chordal and running path consistency on this sparse graph instead of the completion of the given network. In the same way, partial path consistency can be used as the consistency checking step in backtracking algorithms for networks with arbitrary RCC-8 relations resulting in very improved pruning for sparse networks while incurring a penalty for dense networks.

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“…Good heuristic algorithms for triangulating graphs have been developed by Cano and Moral (1995) and Kj rul (1992).…”

Section: Computing a Sampling Distributionmentioning

confidence: 99%

Importance sampling in Bayesian networks using probability trees

Salmerón

Cano

Moral

2000

Computational Statistics & Data Analysis

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In this paper a new Monte-Carlo algorithm for the propagation of probabilities in Bayesian networks is proposed. This algorithm has two stages: in the ÿrst one an approximate propagation is carried out by means of a deletion sequence of the variables. In the second stage a sample is obtained using as sampling distribution the calculations of the ÿrst step. The di erent conÿgurations of the sample are weighted according to the importance sampling technique. We show how the use of probability trees to store and to approximate probability potentials, and a careful selection of the deletion sequence, make this algorithm able to propagate over large networks with extreme probabilities.

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Heuristic algorithms for the triangulation of graphs

Cited by 31 publications

References 12 publications

A Review on Distinct Methods and Approaches to Perform Triangulation for Bayesian Networks

A Review on Distinct Methods and Approaches to Perform Triangulation for Bayesian Networks

Consistency of Chordal RCC-8 Networks

Importance sampling in Bayesian networks using probability trees

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