A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1+ 3 vertices. It is NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a K4-free graph admits a stable cutset. Here we describe algorithms deciding in polynomial time whether a claw-free gr...

Cutset conditioning and clique-tree propagation are two popular methods for performing exact probabilistic inference in Bayesian belief networks. Cutset conditioning is based on decomposition of a subset of network nodes, whereas clique-tree propagation depends on aggregation of nodes. We describe a means to combine cutset conditioning and clique- tree propagation in an approach called aggregat...

The paper investigates the behavior of iterative belief propagation algorithm (IBP) in Bayesian networks with loops. In multiply-connected network, IBP is only guaranteed to converge in linear time to the correct posterior marginals when evidence nodes form a loop-cutset. We propose an-cutset criteria that IBP will converge and compute posterior marginals close to correct when a single value in...

of Thesis presented to COPPE/UFRJ as partia1 fulfillment of the requirements for the degree of Doctor of Science (D.Sc.) Algorithms and Cornplexity of Graph Decomposition Sulamita Klein October, 1994 Thesis Supervisors : Jayme Luiz Szwarcfiter Department : Computing and Systems Engineering We study some types of graph decompositions. Initially, we consider the decoinposition induced by the exis...

The paper studies empirically the time-space trade-off between sampling and inference in the cutset sampling algorithm. The algorithm samples over a subset of nodes in a Bayesian network and applies exact inference over the rest. As the size of the sampling space decreases, requiring less samples for convergence, the time for generating each single sample increases. Algorithm wcutset sampling s...

This paper focuses on probability updates in multiply-connected belief networks. Pearl has designed the method of conditioning, which enables us to apply his algorithm for belief updates in singly-connected networks to multiply-connected belief networks by selecting a loop-cutset for the network and instantiating these loop-cutset nodes. We discuss conditions that need to be satisfied by the se...

Suermondt, H.J. and G.F. Cooper, Initialization for the method of conditioning in Bayesian belief networks (Research Note), Artificial Intelligence 50 (1991) 83-94. The method of conditioning allows us to use Pearl's probabilistic-inference algorithm in multiply connected belief networks by instantiating a subset of the nodes in the network, the loop cutset. To use the method of conditioning, w...

A stable cutset in a graph is a stable set whose deletion disconnects the graph. It was conjectured by Caro and proved by Chen and Yu that any graph with n vertices and at most 2n − 4 edges contains a stable cutset. The bound is tight, as we will show that all graphs with n vertices and 2n− 3 edges without stable cutset arise recursively glueing together triangles and triangular prisms along an...

Metric inequalities, cutset inequalities and Benders feasibility cuts are three families of valid inequalities that have been widely used in different algorithms for network design problems. This article sheds some light on the interrelations between these three families of inequalities. In particular, we show that cutset inequalities are a subset of the Benders feasibility cuts, and that Bende...

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. If the assigned variables constitute a cycle-cutset, the rest of the network is singly-connected and therefore can...