The location problem of interconnected facilities on the line with forbidden gaps is considered. The located facilities are connected among themselves and with gaps. Location in forbidden gaps is not allowed. It is need to minimize the total cost of connections between facilities and between facilities and gaps. It is known that the initial continuous problem is reduced to series discrete subproblems of smaller dimension. In this paper the definition of the local optimum of the problem is introduced. In order that to obtain the local optimum it is necessary to solve some subproblems. The variants of lower bounds of the goal function of the subproblems are proposed. The bounds can be used in the branch and bounds algorithm for solving the subproblems.
We consider a routing problem with constraints. To solve this problem, we employ a variant of the dynamic programming method, where the significant part (that is, the part that matters in view of precedence constraints) of the Bellman function is calculated by means of an independent calculations scheme. We propose a parallel implementation of the algorithm for a supercomputer, where the construction of position space layers for the hypothetical processors is conducted with use of discrete dynamic systems' apparatus.
We consider the strongly NP-hard problem of partitioning a set of Euclidean points into two clusters so as to minimize the sum (over both clusters) of the weighted sum of the squared intracluster distances from the elements of the clusters to their centers. The weights of sums are the cardinalities of the clusters. The center of one of the clusters is given as input, while the center of the other cluster is unknown and determined as the geometric center (centroid), i.e. the average value over all points in the cluster. We analyze the variant of the problem with cardinality constraints. We present an approximation algorithm for the problem and prove that it is a fully polynomial-time approximation scheme when the space dimension is bounded by a constant.
Energy efficiency has become a crucial issue in Computer Science. New hardware and system-based approaches are explored for saving energy in portable battery-operated devices, personal computers, or large server farms. The main mechanisms that have been developed for saving energy are the ability of transitioning the device among multiple power states, and the use of dynamic voltage scaling (speed scaling).
The article deals with the modern approaches to the study of physical and mechanical properties of materials. A brief description is given on the express method for metal-cutting tool health assessment that has been developed within the framework of this approach. The paper suggests ways to improve the performance of by modeling the properties of materials. It presents the methodology for assessing the tool material performance of coated surfaces by acoustic
