This paper presents an any-time scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power is in that it can use any available scheme that bounds the probability of evidence, enhance its performance in an anytime manner, and transform it effectively into bounds for posterior marginals. The scheme is novel in that using the cuts...

A minimal cutset is a cut between source node and sink node such that any proper subset of such minimal cutset is not a cut. A simple method is proposed to determine all minimal cutsets in a network subject to both arc and node failure. The proposed method exactly determines minimal cutsets for an unreliable network from the minimal cutsets of the associated network with perfect nodes and arcs....

We answer a question of Brandstädt et al. by showing that deciding whether a line graph with maximum degree 5 has a stable cutset is NP -complete. Conversely, the existence of a stable cutset in a line graph with maximum degree at most 4 can be decided efficiently. The proof of our NP -completeness result is based on a refinement on a result due to Chvátal that recognizing decomposable graphs w...

In a directed graph, a kernel is a subset of the vertices that is both independent and absorbing. Not all directed graphs have a kernel, and finding classes of graphs having always a kernel or for which deciding the existence of a kernel is polynomial has been the topic of many works in graph theory. We formalize some techniques to build a kernel in a graph with a clique-cutset, knowing kernels...

In this paper, we enhance the MIP formulation for the Network Power Consumption problem, proposed by Giroire et al. We derive cutting planes, extending the wellknown cutset inequalities, and report on preliminary computations.

In this paper we present a cycle-cutset driven stochastic local search algorithm which approximates the optimum of sums of unary and binary potentials, called Stochastic Tree Local Search or STLS. We study empirically two pure variants of STLS against the state-of-the art GLS scheme and against a hybrid.

The rising interest around tractable Probabilistic Graphical Models is due to the guarantees on inference feasibility they provide. Among them, Cutset Networks (CNets) have recently been introduced as models embedding Pearl’s cutset conditioning algorithm in the form of weighted probabilistic model trees with tree-structured models as leaves. Learning the structure of CNets has been tackled as ...

A subset S of V (G) is an independent dominating set of G if S is independent and each vertex of G is either in S or adjacent to some vertex of S. Let i(G) denote the minimum cardinality of an independent dominating set of G. A graph G is k-i-critical if i(G) = k, but i(G+uv) < k for any pair of non-adjacent vertices u and v of G. In this paper, we establish that if G is a connected 3-i-critica...