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Author: Gabor Halasz Publisher: Springer Science & Business Media ISBN: 3642613241 Category : Mathematics Languages : en Pages : 165
Book Description
The problem of uniform distribution of sequences initiated by Hardy, Little wood and Weyl in the 1910's has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called Ramsey theory, a theory of about the same age going back to Schur. Both concern the distribution of sequences of elements in certain collection of subsets. But it was not known until quite recently that the two are closely interweaving bear ing fruits for both. At the same time other fields of mathematics, such as ergodic theory, geometry, information theory, algorithm theory etc. have also joined in. (See the survey articles: V. T. S6s: Irregularities of partitions, Lec ture Notes Series 82, London Math. Soc. , Surveys in Combinatorics, 1983, or J. Beck: Irregularities of distributions and combinatorics, Lecture Notes Series 103, London Math. Soc. , Surveys in Combinatorics, 1985. ) The meeting held at Fertod, Hungary from the 7th to 11th of July, 1986 was to emphasize this development by bringing together a few people working on different aspects of this circle of problems. Although combinatorics formed the biggest contingent (see papers 2, 3, 6, 7, 13) some number theoretic and analytic aspects (see papers 4, 10, 11, 14) generalization of both (5, 8, 9, 12) as well as irregularities of distribution in the geometric theory of numbers (1), the most important instrument in bringing about the above combination of ideas are also represented.
Author: Gabor Halasz Publisher: Springer Science & Business Media ISBN: 3642613241 Category : Mathematics Languages : en Pages : 165
Book Description
The problem of uniform distribution of sequences initiated by Hardy, Little wood and Weyl in the 1910's has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called Ramsey theory, a theory of about the same age going back to Schur. Both concern the distribution of sequences of elements in certain collection of subsets. But it was not known until quite recently that the two are closely interweaving bear ing fruits for both. At the same time other fields of mathematics, such as ergodic theory, geometry, information theory, algorithm theory etc. have also joined in. (See the survey articles: V. T. S6s: Irregularities of partitions, Lec ture Notes Series 82, London Math. Soc. , Surveys in Combinatorics, 1983, or J. Beck: Irregularities of distributions and combinatorics, Lecture Notes Series 103, London Math. Soc. , Surveys in Combinatorics, 1985. ) The meeting held at Fertod, Hungary from the 7th to 11th of July, 1986 was to emphasize this development by bringing together a few people working on different aspects of this circle of problems. Although combinatorics formed the biggest contingent (see papers 2, 3, 6, 7, 13) some number theoretic and analytic aspects (see papers 4, 10, 11, 14) generalization of both (5, 8, 9, 12) as well as irregularities of distribution in the geometric theory of numbers (1), the most important instrument in bringing about the above combination of ideas are also represented.
Author: David M. Nicol Publisher: ISBN: Category : Parallel computers Languages : en Pages : 36
Book Description
Abstract: "This paper describes new mapping algorithms for domain-oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns. We consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network and a relatively slower global network; these partitions heuristically attempt to maximize the fraction of communication carried by the local network. This paper provides an improved algorithm for finding the optimal partition in one dimension, new algorithms for partitioning in two dimensions, and shows that optimal partitioning in three dimensions is NP-complete. We discuss our application of these algorithms to real problems."
Author: Frank Hwang Publisher: World Scientific ISBN: 981270812X Category : Science Languages : en Pages : 363
Book Description
The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The “clustering” problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion.Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory — or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.
Author: Yufei Zhao Publisher: Cambridge University Press ISBN: 1009310941 Category : Mathematics Languages : en Pages : 335
Book Description
An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
Author: Gail Kucera Publisher: CRC Press ISBN: 1000162656 Category : Computers Languages : en Pages : 204
Book Description
A study into the consideration of the temporal dimension of computerized spatial data handling using GIS. The book describes the use of historical and time-variable data as explicit components of the modelling process.
Author: Gabor Halasz
Author: Gabor Halasz
Author: William Bernard Gordon
Author: United States. Congress. House. Committee on Government Operations
Author: Darren Vincent Lee
Author: George E. Andrews
Author: David M. Nicol
Author: Frank Hwang
Author: Yufei Zhao
Author: United States. Patent Office
Author: Gail Kucera