In this paper, we introduce two new algorithms for approximate inference of Bayesian networks that use edge deletion techniques. The first reduces a network to its maximal weight spanning tree using the Kullback-Leibler information divergence as edge weights, and then runs Pearl’s algorithm on the resulting tree for linear-time inference. The second algorithm deletes edges from the triangulated...

Starting with a graph, two players take turns in either deleting an edge or deleting a vertex and all incident edges. The player removing the last vertex wins. We review the known results for this game and extend the computation of nim-values to new families of graphs. A conjecture of Khandhawit and Ye on the nim-values of graphs with one odd cycle is proved. We also see that, for wheels and th...

We consider in this paper the formulation of approximate inference in Bayesian networks as a problem of exact inference on an approximate network that results from deleting edges (to reduce treewidth). We have shown in earlier work that deleting edges calls for introducing auxiliary network parameters to compensate for lost dependencies, and proposed intuitive conditions for determining these p...

Abstract. The energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitr...

We give upper and lower bounds to the number un(Q.) of edges that one can remove from a hypercube without altering its diameter, namely: (n 2) 2”-’ ( ( Ln;2,) ) + 2 < un( Qn) < (n 2)2”_’ + 1 [(2” 1)/(2nl)].

The correlation clustering problem is a fundamental problem in both theory and practice, and it involves identifying clusters of objects in a data set based on their similarity. A traditional modeling of this question as a graph theoretic problem involves associating vertices with data points and indicating similarity by adjacency. Clusters then correspond to cliques in the graph. The resulting...

We present a construction of a visually smooth surface which interpolates to position values and normal vectors of randomly distributed points on a 3D object. The method is local and uses quartic triangular and bicubic quadrilateral patches without splits. It heavily relies on an edge deleting algorithm which, starting from a given triangulation, derives a suitable combination of threeand four ...

one of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (lm) andtransmission electron microscopy (tem). for the lm study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. sections were stained with orcein. for the tem stud...

In recent years, a vast amount of interests has been focused on the formation control of multi-agent system in control engineering field. A multi-agent system consists of multiple interacting mobile agents and this system can be used to solve problems that are difficult or impossible for an individual agent. Based on the interaction topology and the sensing capability of agents, formation contr...

In edge deletion problems, we are given a graph G and a graph property π and the task is to find a subset of edges the deletion of which results in a subgraph of G satisfying the property π. Typically the objective is to minimize the total number of deleted edges while in less common fair versions the objective is to minimize the maximum number of edges removed from a single vertex. We focus on...