Let [n] = {1, 2, . . . , n} and let 2 be the collection of all subsets of [n] ordered by inclusion. C ⊆ 2 is a cutset if it meets every maximal chain in 2, and the width of C ⊆ 2 is the minimum number of chains in a chain decomposition of C. Fix 0 ≤ m ≤ l ≤ n. What is the smallest value of k such that there exists a cutset that consists only of subsets of sizes between m and l, and such that it...

The LOOP CUTSET problem was historically posed by Pearl as a subroutine in Pearl’s algorithm for computing inference in probabilistic networks. The efficiency of the algorithm that solves the probabilistic inference highly depends on the size of the smallest known LOOP CUTSET. This justifies the search for exact algorithms for finding a minimum LOOP CUTSET. In this thesis we are investigating t...

This paper presents an any-time scheme for computing lower and upper bounds on posterior marginals in Bayesian networks. The scheme draws from two previously proposed methods, bounded conditioning (Horvitz, Suermondt, & Cooper 1989) and bound propagation (Leisink & Kappen 2003). Following the principles of cutset conditioning (Pearl 1988), our method enumerates a subset of cutset tuples and app...

Cutset conditioning is one of the methods of solving reasoning tasks for graphical models, especially when space restrictions make inference (e.g., jointree-clustering) algorithms infeasible. The wcutset is a natural extention of the method to a hybrid algoritm that performs search on the conditioning variables and inference on the remaining problems of induced width bounded by w. This paper ta...

Chang, Y. -R. , Lin, H. -Y. , Chen, I. -Y. & Kuo, S. -Y. , A Cut-Based Algorithm for Reliability Analysis of Terminal-Pair Network Using OBDD, Proceedings of the 27th Annual International Conference on Computer Software and Applications, 2003. Fard, N. S. & Lee, T. -H. , Cutset enumeration of network systems with link and node failures, Reliability Engineering and System Safety 1999, pp. 141 14...

Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being compact. We consider the following question: Which ordered sets P can be embedded in an ordered se...

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme r...

In this paper, we develop a polynomial time algorithm to find out all the minilnum cyclic edge cutsets of a 3-regular graph, and therefore to determine the cyclic edge connectivity of a cubic graph. The algorithm is recursive, with complexity bounded by O(n31og2 n). The algorithm shows that the number of mini~um cyclic edge cut sets of a 3-regular graph G is polynornial in v( G) and that the mi...