B. Bájnok and S. Shahriari proved that in 2, the Boolean lattice of order n, the width (the maximum size of an antichain) of a non-trivial cutset (a collection of subsets that meets every maximal chain and does not contain ∅ or [n]) is at least n− 1. We prove that, for n ≥ 5, in the Boolean lattice of order n, given ⌈n2 ⌉− 1 disjoint long chains, we can enlarge the collection to a cutset of wid...

We study maximum-a-posteriori detectors to detect changes in the constant mean vector and covariance matrix of a Gaussian stationary stochastic input driving few nodes network, using remotely located sensor measurements. show that detectors’ performance can be analyzed specific input-to-output gain network system’s transfer function statistics noise asymptotic measurement regime. Using this res...

We present two algorithms for exact and ap­ proximate inference in causal networks. The first algorithm, dynamic conditioning, is a re­ finement of cutset conditioning that has lin­ ear complexity on some networks for which cutset conditioning is exponential. The sec­ ond algorithm, B-conditioning, is an algo­ rithm for approximate inference that allows one to trade-off the quality of approxima...

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or posterior marginals and enhance its performance in an anytime manner. The scheme uses the cutset conditioning principle to tighten existing bounding schemes a...

In this paper we propose a new approach to probabilistic inference on belief networks, global conditioning, which is a simple gener­ alization of Pearl's (1986b) method of loop­ cutset conditioning. We show that global conditioning, as well as loop--cutset condition­ ing, can be thought of as a special case of the method of Lauritzen and Spiegelhalter (1988) as refined by Jensen et al (1990a; 1...

In this paper we study capacitated network design problems, differentiating directed, bidirected and undirected link capacity models. We complement existing polyhedral results for the three variants by new classes of facet-defining valid inequalities and unified lifting results. For this, we study the restriction of the problems to a cut of the network. First, we show that facets of the resulti...

The multicommodity capacitated fixed charge network design problem is a well-known NPhard problem which arises in a wide variety of applications, most notably in transportation and telecommunications. In this paper, we propose to improve the mixed integer programming (MIP) formulation of the problem by using a polyhedral approach. We present a cutting-plane algorithm which incorporates valid in...

Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this article we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim [Oper Res 52 (2004), 35–53]. We present two different mathematical form...

We propose a novel algorithm called RCA_MC, in which we use the breadth first search method (BFS) in conjunction with edge contraction and connectivity properties of a given undirected graph to enumerate and scan all its minimal edge cutsets. It is known that the problem of enumerating all minimal edge cutsets of a given graph is #P-complete. In addition, we introduce the concepts of pivot vert...