in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

This paper addresses the Minimum Linear Ordering Problem (MLOP): Given a nonnegative set function f on a finite set V , find a linear ordering on V such that the sum of the function values for all the suffixes is minimized. This problem generalizes well-known problems such as the Minimum Linear Arrangement, Min Sum Set Cover, Minimum Latency Set Cover, and Multiple Intents Ranking. Extending a ...

A convenient method for defining a quasi-ordering, such as those used for proving termination of rewriting, is to choose the minimum of a set of quasi-orderings satisfying some desired traits. Unfortunately, a minimum in terms of set inclusion can be non-existent even when an intuitive “minimum” exists. We suggest an alternative to set inclusion, called “leanness”, show that leanness is a parti...

An Approximate Minimum Degree ordering algorithm (AMD) for preordering a symmetric sparse matrix prior to numerical factorization is presented. We use techniques based on the quotient graph for matrix factorization that allow us to obtain computationally cheap bounds for the minimum degree. We show that these bounds are often equal to the actual degree. The resulting algorithm is typically much...

In this paper, a mathematical method is proposed to formulate a generalized ordering problem. This model is formed as a linear optimization model in which some variables are binary. The constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. On the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

A recently proposed Minimum Discarded Fill (MDF ) ordering (or pivoting) technique is e ective in nding high quality ILU (`) preconditioners, especially for problems arising from unstructured nite element grids. This algorithm can identify anisotropy in complicated physical structures and orders the unknowns in a \preferred" direction. However, the MDF ordering is costly, when ` increases. In t...