This paper concerns the following problem: given a set of multi-attribute records, a fixed number of buckets and a two-disk system, arrange the records into the buckets and then store the buckets between the disks in such a way that, over all possible orthogonal range queries (ORQs), the disk access concurrency is maximized. We shall adopt the multiple key hashing (MKH) method for arranging records into buckets and use the disk modulo (DM) allocation method for storing buckets onto disks. Since the DM allocation method has been shown to be superior to any other allocation methods for allocating an MKH file onto a two-disk system for answering ORQs, the real issue is knowing how to determine an optimal way for organizing the records into buckets based upon the MKH concept.
A performance formula that can be used to evaluate the average response time, over all possible ORQs, of an MKH file in a two-disk system using the DM allocation method is first presented. Based upon this formula, it is shown that our design problem is related to a notoriously difficult problem, namely the Prime Number Problem. Then a performance lower bound and an efficient algorithm for designing optimal MKH files in certain cases are presented. It is pointed out that in some cases the optimal MKH file for ORQs in a two-disk system using the DM allocation method is identical to the optimal MKH file for ORQs in a single-disk system and the optimal average response time in a two-disk system is slightly greater than one half of that in a single-disk system. 相似文献
The permeability and lag time for a heterogeneous diffusion system, in which the diffusivity and partition coefficient for the diffusant are dependent on position, are formulated in terms of a linear asymptotic analysis. A repeated integration of the diffusion equation is used to obtain the time dependence of the total solute release into the receiver, Q(t). The asymptotic form of Q(t) is linear in time. The slope, and intercept of this linear asymptote with the time axis, respectively, give formulas for the steady-state permeability and lag time. These formulas are then applied to diffusion systems of multiple laminates, consisting of a series of different homogeneous slabs. Thus, for the first time, a concise treatment of diffusion in multiple laminates is obtained. The formulas are also applied to periodic laminates, consisting of a series of identical slabs, but with position-dependent diffusivity and partition coefficient. We found that the lag time can be well approximated by (nh))2/(6Deff), where n and h are, respectively, the number and thickness of individual lamella, and Deff is an effective diffusivity, for which a relation in terms of the local property distributions is obtained. This approximation becomes more accurate with increasing number of lamellae. At n = 5, the relative error is already within 4%. Finally a procedure is discussed for readily obtaining the lag time for periodic structures consisting of a serial repetition of a multi-laminate. 相似文献
Review of book: Stephen Mitchell. Can Love Last? The Fate of Romance Over Time. New York: Norton, 2002, 223 pp. Reviewed by Timothy J. Zeddies. (PsycINFO Database Record (c) 2010 APA, all rights reserved) 相似文献