Let P6 denote the induced path on six nodes. We prove that if a perfect graph G contains P6 as an induced subgraph but not two families introduced by Conforti and Cornuéjols then G is bipartite or disconnected, or % G has a star cutset. r 2002 Elsevier Science (USA). All rights reserved.

Inference on factor graphs with loops with the standard forwardbackward algorithm, can give unpredictible results as messages can travel indefinitely in the system with no guarantee on convergence. We apply the exact method of cutset conditioning to Factor Graphs with loops starting from a fully developed three-variable example and providing comments and suggestions for distributed implementati...

Symmetric networks designed for energy minimization such as Boltzman machines and Hop eld nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, nding a global solution (i.e., a global minimum for the energy function) is not guaranteed and even a local solution may take an exponential number of steps. We propose an ...

Some experiments on randomly generated partial constraint satisfaction problems as well as an example from the domain of real world nurse rostering illustrate the advantage of the cyclecutset method as a repair step in iterative search. These results motivate the integration of adopted algorithms on solving tree-structured constraint problems and the cycle-cutset method into modern constraint-b...

Let G be a minimal imperfect P 5-free graph (i.e. a minimal imperfect graph not containing a path on 5 vertices as induced subgraph) and let S be a minimal cutset of G. In this paper we study several properties of such cutsets, in particular we prove that the subgraph induced by S is connected, contains a P 4 , cannot induce a bipartite subgraph of G .... As a by-product we also give a structur...

This paper is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specificially, we propose the use of a directed cutset method, weighted minimum cut, to exploit the structure of the computional graph of the nonlinear system. This allows for the efficient determination of the Jacobian matrix using AD software. We discuss t...

In this paper we study a certain cardinality constrained packing integer program which is motivated by the problem of dimensioning a cut in a two-layer network. We prove NP-hardness and consider the facial structure of the corresponding polytope. We provide a complete description for the smallest nontrivial case and develop two general classes of facet-defining inequalities. This approach exten...

We study the arbitrarily varying relay channel, and establish the cutset bound and partial decode-forward bound on the random code capacity. We further determine the random code capacity for special cases. Then, we consider conditions under which the deterministic code capacity is determined as well. In addition, we consider the arbitrarily varying Gaussian relay channel with sender frequency d...