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
File swarming (or file sharing) is one of the most important applications in P2P networks. In this paper, we propose a stochastic framework to analyze a file-swarming system under realistic setting: constraints in upload/download capacity, collaboration among peers and incentive for chunk exchange. We first extend the results in the coupon system [L. Massoulie, M. Vojnovic, Coupon replication systems, in: Proc. ACM SIGMETRICS, Banff, Alberta, Canada, 2005] by providing a tighter performance bound. Then we generalize the coupon system by considering peers with limited upload and download capacity. We illustrate the last-piece problem and show the effectiveness of using forward error-correction (FEC) code and/or multiple requests to improve the performance. Lastly, we propose a framework to analyze an incentive-based file-swarming system. The stochastic framework we propose can serve as a basis for other researchers to analyze and design more advanced features of file-swarming systems. 相似文献