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Random Algorithms for the Loop Cutset Problem
 Journal of Artificial Intelligence Research
, 1999
"... We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after ..."
Abstract

Cited by 77 (1 self)
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We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c \Delta 6 k kn) steps, with probability at least 1 \Gamma (1 \Gamma 1 6 k ) c6 k , where c ? 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm, called WRA, often finds a loop cutset that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known. 1
Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference
, 1998
"... A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomialtime algorithms are provided for approximating the problem of finding a feedback ve ..."
Abstract

Cited by 30 (3 self)
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A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomialtime algorithms are provided for approximating the problem of finding a feedback vertex set of G with a smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4 \Gamma (2=n). This improves a previous algorithm which achieved an approximation factor of O( p log n) for this case. For general vertex weights, the performance ratio becomes minf2\Delta 2 ; 4 log 2 ng where \Delta denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10. An interesting special case of weighted graphs where a performance ratio of 4 \Gamma (2=n) is achieved is the one where a prescribed subset of the vertices, so called blackout vertices, is not allowed to participate in any feedback verte...