In this paper a sufficient condition is given for minimal routing in n-dimensional (n-D) meshes with faulty nodes contained in a set of disjoint fault regions. It is based on an early work of the author on minimal routing in low-dimensional meshes (such as 2-D meshes with faulty blocks). Unlike many traditional models that assume all the nodes know global fault distribution, our approach is bas...

In this paper we deal with iterative numerical methods to solve linear systems arising in continuous-time Markov chain (CTMC) models. We develop an algorithm to dynamically tune the relaxation parameter of the successive over-relaxation method. We give a sufficient condition for the Gauss-Seidel method to converge when computing the steady-state probability vector of a finite irreducible CTMC, ...

Many of the existing tractability results for parameterised problems which involve finding or counting subgraphs with particular properties rely on bounding the treewidth of the minimal subgraphs having the desired property. In this paper, we give a number of hardness results – for decision, approximate counting and exact counting – in the case that this condition on the minimal subgraphs havin...

A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration. It is also observed that there exist reduced reversible automata which are not minimal, in the sense that all the automata obtained by merging some of their e...

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

in this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. numerical examples are presented to illustrate the proposed method.

a common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the weierstrass canonical form. the weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. the present ...

Abstract: The intersection graph of a set of chords on a circle is called a circle graph. This class of graphs admits some interesting subclasses, such as: Helly circle graphs, clique-Helly circle graphs, unit circle graphs and proper circular-arc graphs. In this paper, we prove some inclusion relations among these subclasses. A necessary condition for a graph being a Helly circle graph is show...

In this paper we analyze the numerical behavior of several minimum residual methods, which are mathematically equivalent to the GMRES method. Two main approaches are compared: the one that computes the approximate solution (similar to GMRES) in terms of a Krylov space basis from an upper triangular linear system for the coordinates, and the one where the approximate solutions are updated with a...