We discuss an efficient implementation of the iterative proportional scaling procedure in the multivariate Gaussian graphical models. We show that the computational cost can be reduced by localization of the update procedure in each iterative step by using the structure of a decomposable model obtained by triangulation of the graph associated with the model. Some numerical experiments demonstra...

We show that the traces of recently introduced dynamic programming algorithms for #SAT can be used to construct structured deterministic DNNF (decomposable negation normal form) representations of propositional formulas in CNF (conjunctive normal form). This allows us prove new upper bounds on the complexity of compiling CNF formulas into structured deterministic DNNFs in terms of parameters su...

We discuss an efficient implementation of the iterative proportional scaling procedure in the multivariate Gaussian graphical models. We show that the computational cost can be reduced by localization of the update procedure in each iterative step by using the structure of a decomposable model obtained by triangulation of the graph associated with the model. Some numerical experiments demonstra...

In this paper we show that primitive data swaps or moves are the only moves that have to be included in a Markov basis that links all the contingency tables having a set of fixed marginals when this set of marginals induce a decomposable independence graph. We give formulas that fully identify such Markov bases and show how to use these formulas to dynamically generate random moves.

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i  v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih  v  v  v  over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...

A graph G = (V,E) is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to |V |, there is a sequence of vertex-disjoint subsets of V whose orders are given by τ , and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs ...

We consider dynamic data structures in which updates rebuild a static solution. Space bounds for persistent versions of these structures can often be reduced by using an offline persistent data structure in place of the static solution. We apply this technique to decomposable search problems, to dynamic linear programming, and to maintaining the minimum spanning tree in a dynamic graph. Our alg...