## Random Algorithms for the Loop Cutset Problem (1999)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 77 - 1 self |

### BibTeX

@INPROCEEDINGS{Becker99randomalgorithms,

author = {Ann Becker and Reuven Bar-Yehuda and Dan Geiger},

title = {Random Algorithms for the Loop Cutset Problem},

booktitle = {Journal of Artificial Intelligence Research},

year = {1999},

pages = {60--68},

publisher = {Morgan Kaufmann}

}

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### Abstract

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

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Citation Context ...and the other performs probabilistic computations. For example, the clique tree algorithm requires us to first find a "good" clique tree and then perform probabilistic computations on the clique tree =-=[LS88]-=-. Pearl's method of conditioning requires us first to find a "good" loop cutset and then perform a calculation for each loop cutset [Pe86, Pe881. Finally, Shachter's algorithm requires us to find a "g... |

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Citation Context ...ause the second phase of the conditioning algorithm, which is repeated for many iterations, uses a procedure of such complexity. The same considerations apply also to constraint satisfaction problems =-=[De90]-=-. In this paper we describe several random algorithms that compute a loop cutset. As in [BGNR94], our solution is based on a reduction to the Weighted Feedback Vertex Set (WFVS) Problem, defined below... |

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Citation Context ... called the FVS problem. The decision version associated with the FVS problem is known to be NP-complete [GJ79, pp. 191-1921. Note that also the problem of finding a minimum loop cutset is NPcomplete =-=[SC90]-=-. Our random algorithm for finding a FVS, called REPEATEDWGUESSI, outputs a minimum weight FVS, after O(c . Gkkn) steps, with probability at least 1 -50 Becker, Bar-Yehuda, and Geiger (1- &)c~', wher... |

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Citation Context ...is harder to analyze and its investigation is mostly experimental. We show empirically that the actual run time of WRA is comparable to a Modified Greedy Algorithm (MGA), devised by Becker and Geiger =-=[BG96]-=-, which is the best available deterministic algorithm for finding close to optimal loop cutsets, and yet, the output of WRA is often closer to the minimum loop cutest than the output of MGA. The rest ... |

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Citation Context ... - The proof is an immediate corollary of Theorem 3. The choise of Max and c depend on the application. A decision-theoretic approach for selecting such values for any-time algorithms is discussed in =-=[BH90]-=-. 4 Experimental results The experiments compared the outputs of WRA visB-vis a greedy algorithm GA and a modified greedy algorithm MGA [BG96] based on randomly generated graphs and on some real graph... |

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