Decision-DNNF is a strict subset of decomposable negation normal form (DNNF) that plays a key role in analyzing the complexity of model counters (the searches performed by these counters have their traces in Decision-DNNF). This paper presents a number of results on Decision-DNNF. First, we introduce a new notion of CNF width and provide an algorithm that compiles CNFs into Decision-DNNFs in ti...

We propose an objective Bayesian method for the comparison of all Gaussian directed acyclic graphical models defined on a given set of variables. The method, which is based on the notion of fractional Bayes factor, requires a single default (typically improper) prior on the space of unconstrained covariance matrices, together with a prior sample size hyper-parameter, which can be set to its min...

In a model selection procedure where many models are to be compared, computational efficiency is critical. For acyclic digraph (ADG) Markov models (aka DAG models or Bayesian networks), each ADG Markov equivalence class can be represented by a unique chain graph, called an essential graph (EG). This parsimonious representation might be used to facilitate selection among ADG models. Because EGs ...

We rst present VLSI algorithms that run in O(n 2) steps for nding (and reporting) a fundamental set of cycles and a fundamental set of cutsets of an undirected graph on an nxn mesh of processors (SIMD). Both algorithms are decomposable and run in O(n 4 =k 2) steps for a graph with n vertices when the size of the mesh-connected computer is kxk and k < n. An idea similar to the one used in nding ...

Let G be a connected graph that is the edge-disjoint union of two paths of length n, where n ≥ 2. Using a result of Thomason on decompositions of 4-regular graphs into pairs of Hamiltonian cycles, we prove that G has a third path of length n. The “two-path conjecture” states that if a graph G is the edge-disjoint union of two paths of length n with at least one common vertex, then the graph has...

We define the decomposition property for partial actions of discrete groups on C⁎-algebras. Decomposable systems appear naturally in practice, and many commonly occurring can be decomposed into with property. For instance, any action a finite group is an iterated extension decomposable systems. Partial are always globalizable amenable, regardless acting group, their globalization explicitly des...