V. Samoladas and D. P. Miranker. A lower bound theorem for indexing schemes and its application to multidimensional range queries. In Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 44--51. ACM Press, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....O(log N) internal memory search term, and an O(T=B) reporting term accounting for the O(T=B) I Os needed to report T elements. Recently, the above bounds have been obtained for a number of problems (e. g [30, 26, 149, 5, 47, 87] but higher lower bounds have also been established for some problems [141, 26, 93, 101, 106, 135, 102]. We discuss these results in later sections. B trees come in several variants, like B and B trees (see e.g. 35, 63, 95, 30, 104, 3] and their references) A basic B tree is a Theta(B) ary tree (with the root possibly having smaller degree) built on top of Theta(N=B) leaves. The degree of ....

.... in a natural external memory version of the pointer machine model [53] A similar bound in a slightly different model where the search component of the query is ignored was proved by Arge et al. 26] This indexability model was defined by Hellerstein et al. 93] and considered by several authors [101, 106, 135]. Based on a sub optimal but linear space structure for answering 3 sided queries, Subramanian and Ramaswamy developed the P range tree that uses optimal O( N log(N=B) B log log B N ) space but uses more than the optimal O(log B N T=B) 1 In fact, this bound even holds for a query bound of ....

V. Samoladas and D. Miranker. A lower bound theorem for indexing schemes and its application to multidimensional range queries. In Proc. ACM Symp. Principles of Database Systems, pages 44--51, 1998.

.... where the instance I consists of the regular grid (the k Theta k grid points) It was shown that these workloads have non trivial tradeoff; an indexing scheme that achieves access overhead a must have storage redundancy r = Omega Gamma460 B= a 2 log a) 1 2 This result was improved in [13], which gave the exact trade off for these workloads: r = Theta(log B= log a) For the d dimensional range queries where the instance I consists of the regular grid: the trade off is given by r = Theta( log B= log a) d Gamma1 ) In another direction, 6] studied workloads of rangequeries on ....

V. Samoladas and D. P. Miranker. A Lower Bound Theorem for Indexing Schemes and its Application to Multidimensional Range Queries. In Proc. 17th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 44--51, Seattle, June 1998.

....tradeoff. One necessary property is suggested by Theorem 1: Some pairs or points (and in general constant size sets of points) must be contained in many queries of size B. 5 High Dimensional Trade offs Finally, we state an extension of the main result of [6] to many dimensions. Independently, [17] came up with more comprehensive results of this sort. The proof is similar to that in [6] and is omitted from this abstract. Theorem 4 For the d dimensional workload with point set f1; n 1=d g d , the access overhead a and the redundancy r must satisfy r cd log d Gamma1 B 2a d ....

V. Samoladas and D. P. Miranker. A Lower Bound Theorem for Indexing Schemes and its Application to Multidimensional Range Queries. This conference.

....Q as the ratio between the access cost of Q over djQj=Be, where djQj=Be is the minimum possible number of blocks that answer the query Q. The access overhead ff of the indexing scheme S is defined as the maximum access overhead over all possible queries. Note that 1 ff B. Samoladas and Miranker [79] prove that for any workload W , if we fix the access overhead ff, then if we can find a set of M queries that have large size (that is, greater than B) and small intersection (that is, O( B ff 2 ) then the storage redundancy is Omega Gamma MB n ) They apply this theorem for the case of ....

V. Samoladas and D. P. Miranker. A lower bound theorem for indexing schemes and its application to multidimensional range queries. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 44--51, 1998.

....a uniform shape for the chunks that reduces the average number of blocks fetched for a specified access pattern. The chunks are always stored in axis order, and [21] additionally determines a good ordering of the array axes to reduce average seek time, given the access pattern. It is well known [11, 18, 22] that there is no good ordering of data points in a multi dimensional space that will permit arbitrary range queries to be answered efficiently. 22] established, given a uniform distribution of key values, that a k attribute selection on a database with N records has a file access cost of O(N ....

V. Samoladas and D. P. Miranker. A lower bound theorem for indexing schemes and its application to multidimensional range queries. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 44--51, 1998.

....of data items in queries. In particular, this definition makes no distinction between query specifications and their outputs a query is defined by the set of items it retrieves. This abstraction leads to simplified systems [HNP95] frameworks for discussing the hardness of indexing problems [HKP97, SM98, KT98], and domain independent methodologies for measuring the performance of queries over indexes [KSH98] A natural extension of this idea is to test indexes in a similarly domain independent manner, by choosing randomly from the space of logical queries. In particular, a random logical query is ....

Vasilis Samoladas and Daniel P. Miranker. A Lower Bound Theorem for Indexing Schemes and its Application to Multidimensional Range Queries In Proc. 17th ACM PODS Symposium on Principles of Database Systems, Seattle, 1998.

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V. Samoladas and D. P. Miranker. A lower bound theorem for indexing schemes and its application to multidimensional range queries. In Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 44--51. ACM Press, 1998.

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