The page number problem is to determine the minimum number of pages in a book in which a graph G can be embedded with the vertices placed in a sequence along the spine and the edges on the pages of the book such that no two edges cross each other in any drawing. In this paper we have (a) statistically evaluated five heuristics for ordering vertices on the spine for minimum number of edge crossi...

this study aims to deal with a more realistic combined problem of project scheduling and material ordering. the goal is to minimize the total material holding and ordering costs by determining the starting time of activities along with material ordering schedules subject to some constraints. the problem is first mathematically modelled. then a hybrid simulated annealing and genetic algorithm is...

This paper generalises the concept of vertex pancyclic graphs. We define a graph as set-pancyclic if for every set S of vertices there is a cycle of every possible length containing S. We show that if the minimum degree of a graph exceeds half its order then the graph is set-pancyclic. We define a graph as k-ordered-pancyclic if, for every set S of cardinality k and every cyclic ordering of S, ...

The minimum cost homomorphism problem has arisen as a natural and useful optimization problem in the study of graph (and digraph) coloring and homomorphisms: it unifies a number of other well studied optimization problems. It was shown by Gutin, Rafiey, and Yeo that the minimum cost problem for homomorphisms to a digraph H that admits a so-called extended MinMax ordering is polynomial time solv...

The maximum and minimum of a sample from a probability distribution are extremely important random variables in many areas of psychological theory, methodology, and statistics. For instance, the behavior of the mean of the maximum or minimum processing time, as a function of the number of component random processing times (n), has been studied extensively in an effort to identify the underlying...

Local algorithms for obtaining a pivot ordering for sparse symmetric coefficient matrices are reviewed together with their mathematical background and appropriate data structures. Recently proposed heuristics as well as improvements to them are discussed, and their performance, mainly in terms of the resulting number of factorization operations, is compared with that of the Minimum Degree and t...

Scan chain insertion can have large impact on routability, wirelength and timing. We propose a routing-driven and timing-aware methodology for scan insertion with minimum wirelength. We take into account timing slacks at all sinks that are affected by scan insertion, to achieve a scan chain ordering that meets timing and has smallest wirelength. For the case where sink timing is not met, we als...

Let H be a fixed graph without loops. We prove that if H is a co-circular arc bigraph then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm; otherwise the minimum cost homomorphism problem to H is known to be not approximable. This solves a problem posed in an earlier paper. For the purposes of the approximation, we provide a new charact...

We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one particle (in higher dimensions). In quantum mechanics, we find that diffraction effects introduce a minimum inaccuracy to which the temporal order-of-arriva...

the planning of production and control of inventory problem is one of most important problems that companies are face with them. some times inattention to uncertainty in these problems causes to increase of costs of inventory control systems. one of the important ways encountering to uncertainty is the widespread of fuzzy sets instead of crisp numbers because in this approach, we can determine ...