Declustering schemes allocate data blocks among multiple disks to enable parallel retrieval. Given a declustering scheme D, its response time with respect to a query Q, rt(Q), is defined to be the maximum number of disk blocks of the query stored by the scheme in any one of the disks. If |Q| is the number of data blocks in Q and M is the number of disks then rt(Q) is at least |Q|/M. One way to evaluate the performance of D with respect to a set of queries Q is to measure its additive error- the maximum difference between rt(Q) from |Q|/M over all range queries Q ∈ Q. In this paper, we consider the problem of designing declustering schemes for uniform multidimensional data arranged in a d-dimensional grid so that their additive errors with respect to range queries are as small as possible. It has been shown that such declustering schemes will have an additive error of Ω(log M) when d = 2 and Ω(log d−1 2 M) when d> 2 with respect to range queries. Asymptotically optimal declustering schemes exist for 2dimensional data. For data in larger dimensions, however, the best bound for additive errors is O(M d−1), which is extremely large. In this paper, we propose the two declustering schemes based on low discrepancy points in d-dimensions. When d is fixed, both schemes have an additive error of O(log d−1 M) with respect to range queries provided certain conditions are satisfied: the first scheme requires d ≥ 3 and M to be a power of a prime where the prime is at least d while the second scheme requires the size of the data to grow within some polynomial of M, with no restriction on

A common technique used to minimize I/O in data intensive applications is data declustering over parallel servers. This technique involves distributing data among several disks so as to parallelize query retrieval and thus, improve performance. We focus on optimizing access to large spatial data, and the most common type of queries on such data, i.e., range queries. An optimal declustering scheme is one in which the processing for all range queries is balanced uniformly among the available disks. It has been shown that single copy based declustering schemes are non-optimal for range queries. In this paper, we integrate replication in conjunction with parallel disk declustering for efficient processing of range queries. We note that replication is largely used in database applications for several purposes like load balancing, fault tolerance and availability of data. We propose theoretical foundations for replicated declustering and propose a class of replicated declustering schemes, periodic allocations, which are shown to be strictly optimal for a number of disks. We propose a framework for replicated declustering, using a limited amount of replication and provide extensions to apply it on real data, which include arbitrary grids and a large number of disks. Our framework also provides an effective indexing scheme that enables fast identification of data of interest in parallel servers. In addition to optimal processing of single queries, we show that this framework is effective for parallel processing of multiple queries. We present experimental results comparing the proposed replication scheme to other techniques for both single queries and multiple queries, on synthetic and real data sets.

Abstract—Declustering distributes data among parallel disks to reduce the retrieval cost using I/O parallelism. Many schemes were proposed for the single-copy declustering of spatial data. Recently, declustering using replication gained a lot of interest and several schemes with different properties were proposed. An in-depth comparison of major schemes is necessary to understand replicated declustering better. In this paper, we analyze the proposed schemes, tune some of the parameters, and compare them for different query types and under different loads. We propose a three-step retrieval algorithm for the compared schemes. For arbitrary queries, the dependent and partitioned allocation schemes perform poorly; others perform close to each other. For range queries, they perform similarly with the exception of smaller queries in which random duplicate allocation (RDA) performs poorly and dependent allocation performs well. For connected queries, partitioned allocation performs poorly and dependent allocation performs well under a light load. Index Terms—Declustering, parallel I/O, spatial range query, Latin square. 1

Declustering is a common technique used to reduce query response times. Data is declustered over multiple disks and query retrieval can be parallelized. Most of the research on declustering is targeted at spatial range queries and investigates schemes with low additive error. Recently, declustering using replication has been proposed to reduce the additive overhead. Replication significantly reduces retrieval cost of arbitrary queries. In this paper, we propose a disk allocation and retrieval mechanism for arbitrary queries based on design theory. Using the proposed c-copy replicated declustering scheme, (c − 1)k 2 + ck buckets can be retrieved using at most k disk accesses. Retrieval algorithm is very efficient and is asymptotically optimal with �(|Q|) complexity for a query Q. In addition to the deterministic worst-case bound and efficient retrieval, proposed algorithm handles nonuniform data, high dimensions, supports incremental declustering and has good faulttolerance property. Experimental results show the feasibility of the algorithm.

A common technique for improving performance in a database is to decluster the database among multiple disks so that data retrieval can be parallelized. In this paper we focus on answering range queries in a multidimensional database (such as a GIS), where each of its dimensions is divided uniformly to obtain tiles which are placed on different disks; there has been a significant amount of research for this problem (a subset of which is [1,2,3,4,5,6,7,8,9,11,12,13,14,15]). A declustering scheme would be optimal if any range query could be answered by doing no more than ⌈ # of tiles inside the range/ # of disks ⌉ retrievals from any one disk. However, it was shown in [1] that this is not achievable in many cases even for two dimensions, and therefore much of the research in this area has focused on developing schemes that performed close to optimal. Recently, the idea of using replication (i.e. placing records on more than one disk) to increase performance has been introduced. [7, 12,13,15]. If replication is used, a retrieval schedule (i.e. which disk to retrieve each tile from) must be computed whenever a query is being processed. In this paper we introduce a class of replicated schemes where the retrieval schedule can be computed in time O( # of tiles inside the query’s range), which is asymptotically equivalent to query retrieval for the non-replicated case. Furthermore, this class of schemes has a strong performance advantage over non-replicated schemes, and several schemes are introduced that are either optimal or are optimal plus a constant additive factor. Also presented in this paper is a strictly optimal scheme for any number of colors that requires the lowest known level of replication of any such scheme.

Watermarking is a frequently used tool for digital rights management. An example of this is using watermarks to place ownership information into an object. There are many instances where placing multiple watermarks into the same object is desired. One mechanism that has been proposed for doing this is segmenting the data into a grid and placing watermarks into different regions of the grid. This is particularly suited for images and geographic information systems (GIS) databases as they already consist of a fine granularity grid (of pixels, geographic regions, etc.); a grid cell for watermarking is an aggregation of the original fine granularity cells. An attacker may be interested in only a subset of the watermarked data, and it is crucial that the watermarks survive in the subset selected by the attacker. In the kind of data mentioned above (images, GIS, etc.) such an attack typically consists of cropping, e.g. selecting a geographic region between two latitudes and longitudes (in the GIS case) or a rectangular region of pixels (in an image). The contribution of this paper is a set of schemes and their analysis for multiple watermark placement that maximizes resilience to the above mentioned cropping attack. This involves the definition of various performance metrics and their use in evaluating and comparing various placement schemes.

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Abstract. In this paper we study the problem of declustering two-dimensional datasets with replication over parallel devices to improve range query performance. The related problem of declustering without replication has been well studied. It has been established that strictly op-timal declustering schemes do not exist if data is not replicated. In addi-tion to the usual problem of identifying a good allocation, the replicated version of the problem needs to address the issue of identifying a good retrieval schedule for a given query. We address both problems in this paper. An efficient algorithm for finding a lowest cost retrieval schedule is developed. This algorithm works for any query, not just range queries. Two replicated placement schemes are presented – one that results in a strictly optimal allocation, and another that guarantees a retrieval cost that is either optimal or 1 more than the optimal for any range query. 1

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