Let f be a set function on a finite set V . A pair {u, v} ⊆ V is called flat in f if f(X) ≥ minx∈X f({x}) holds for all subsets X ⊆ V with |X ∩ {u, v}| = 1. A subset X ⊆ V is called an extreme subset of f if f(Y ) > f(X) holds for all nonempty and proper subsets Y of X. In this paper, we first define a minimum degree ordering (MD ordering) of V , and show that the last two elements in an MD ord...

In this paper, we perform a comprehensive evaluation of ordering, partitioning, and factorization algorithms under a uni ed framework. Previous research in distributed, sparse Cholesky factorization has considered each of the stages in the factorization process | ordering, partitioning and numerical factorization | in isolation. However, due to the strong dependencies between the stages, it is ...

In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of “good” methods. These comparisons often led us to consider FC or FC-CBJ associated with a “minimum domain” variable ordering heuristic as the...

The cost minimization problem in an agency model with imperfect monitoring is considered. Under the ®rst order approach, this can be stated as a convex minimization problem with linear inequality and equality constraints in a generally in®nite dimensional function space. We apply the Fenchel Duality Theorem, and obtain as a dual problem a concave maximization problem of ®nite dimension. In part...

The solution of chemical process simulation and optimization problems on today's high performance supercomputers requires algorithms that can take advantage of vector and parallel processing when solving the large, sparse matrices that arise. The frontal method can be highly e cient in this context due to its ability to make use of vectorizable dense matrix kernels on a relatively small frontal...

The cyclic matching sequenceability of a simple graph G, denoted cms ( G ) , is the largest integer s for which there exists ordering edges so that every set consecutive forms matching. In this paper we consider minimum k-regular graphs. We completely determine 2-regular graphs, and give bounds k ⩾ 3.

generally ordering policies are done by two methods, including fix order quantity (foq) and fix order period (fop). these methods are static and either the quantity of ordering or the procedure of ordering is fixing in throughout time horizon. in real environments, demand is varying in any period and may be considered as uncertainty. when demand is variable in any period, the traditional and st...

We show that a minimum ll-in ordering of a graph can be determined in linear time if it can be modularly decomposed into chordal graphs. This generalizes results of 2]. We show that the treewidth of these graphs can be determined in O((n + m) log n) time.

We perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected cost from its minimum) have been identified and its magnitude is studied by establishing a lower bound. We found the newsvendor model to be sensitive to sub-optimal ordering decisions.