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
A method for detection of multiple open cracks in a slender Euler-Bernoulli beams is presented based on frequency measurements. The method is based on the approach given by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841], transverse vibration modelling through transfer matrix method and representation of a crack by rotational spring. The beam is virtually divided into a number of segments, which can be decided by the analyst, and each of them is considered to be associated with a damage parameter. The procedure gives a linear relationship explicitly between the changes in natural frequencies of the beam and the damage parameters. These parameters are determined from the knowledge of changes in the natural frequencies. After obtaining them, each is treated in turn to exactly pinpoint the crack location in the segment and determine its size. The forward, or natural frequency determination, problems are examined in the passing. The method is approximate, but it can handle segmented beams, any boundary conditions, intermediate spring or rigid supports, etc. It eliminates the need for any symbolic computation which is envisaged by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841] to obtain mode shapes of the corresponding uncracked beams. The proposed method gives a clear insight into the whole analysis. Case studies (numerical) are presented to demonstrate the method effectiveness for two simultaneous cracks of size 10% and more of section depth. The differences between the actual and predicted crack locations and sizes are less than 10% and 15% respectively. The numbers of segments into which the beam is virtually divided limits the maximum number of cracks that can be handled. The difference in the forward problem is less than 5%. 相似文献
Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process. 相似文献