In this paper we present Stochastic Tree-based Local Search or STLS, a local search algorithm combining the notion of cycle-cutsets with the well-known Belief Propagation to approximate the optimum of sums of unary and binary potentials. This is done by the previously unexplored concept of traversal from one cutset to another and updating the induced forest, thus creating a local search algorit...

We develop a new upper bound on the capacity of relay channel that is tighter than previously known bounds. This proved using traditional weak converse techniques involving mutual information inequalities and Gallager-type explicit identification auxiliary random variables. show strictly all previous bounds for Gaussian with non-zero gains. When specialized to orthogonal receiver components, re...

Multiply sectioned Bayesian networks (MSBNs) provide one framework for agents to estimate the state of a domain. Existing methods for multi-agent inference in MSBNs are based on linked junction forests (LJFs). The methods are extensions of message passing in junction trees for inference in singleagent Bayesian networks (BNs). We consider extending other inference methods in single-agent BNs to ...

In this paper, we provide an improved lower bound on the rate achieved by noisy network coding in arbitrary Gaussian relay networks, whose gap to the cutset upper bound depends on the network not only through the total number of nodes but also through the degrees of freedom of the min cut of the network. We illustrate that for many networks this refined lower bound can lead to a better approxim...

Fault trees are widely used for safety analysis. In this context fault trees are considered as boolean formulas. The major problem of their assessment is the combinatorial explosion in time and space. Binary Decision Diagrams (BDD) are the state-of-the-art compact representation for boolean formulas (?; ?). By limiting combinatorial growth, this representation makes possible the assessment of c...

In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of infeasible 0,1 vectors that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal...

In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of infeasible 0,1 vectors that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal...

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite...

In 1988, Chvátal and Sbihi [4] proved a decomposition theorem for claw-free perfect graphs. They showed that claw-free perfect graphs either have a clique-cutset or come from two basic classes of graphs called elementary and peculiar graphs. In 1999, Maffray and Reed [6] successfully described how elementary graphs can be built using line-graphs of bipartite graphs using local augmentation. How...

A bilevel image can be modeled by the Markov random field (MRF). Let G = (V,E) be an 8-connected graph, where V and E denote the nodes (vertices) and edges, modeling the pixels and the connectivities in an image, respectively. The MRF with 2-point cliques is defined on the 8-connected graph. The 2-point cliques consist of horizontal, vertical and diagonal neighboring nodes (Figure 1a). A node i...