Simple algorithms for minimal triangulation of a graph and backward selection of a decomposable Markov network

Authors:
Mauro Mezzini;Marina Moscarini
Affiliations:
Department of Computer Science, Sapienza University of Rome, Italy11http://www.di.uniroma1.it/;Department of Computer Science, Sapienza University of Rome, Italy11http://www.di.uniroma1.it/
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

In this paper we propose a simple algorithm called CliqueMinTriang for computing a minimal triangulation of a graph. If F is the set of edges that is added to G to make it a complete graph K"n then the asymptotic complexity of CliqueMinTriang is O(|F|(@d^2+|F|)) where @d is the degree of the subgraph of K"n induced by F. Therefore our algorithm performs well when G is a dense graph. We also show how to exploit the existing minimal triangulation techniques in conjunction with CliqueMinTriang to efficiently find a minimal triangulation of nondense graphs. Finally we show how the algorithm can be adapted to perform a backward stepwise selection of decomposable Markov networks; the resulting procedure has the same time complexity as that of existing similar algorithms.