Elias Koutsoupias and D. S. Taylor. Tight Bounds for 2-Dimensional Indexing Schemes. Proceedings of the seventeenth ACM SIGACTSIGMOD -SIGART symposium on Principles of database systems, page 52-58. June 1998, Seattle, WA USA.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Novel Indexing Scheme for XML Data by Extending the GiST Framework Cong Yu: congy engin.umich.edu Hai Huang: haih engin.umich.edu Hongmei Ge: hge engin.umich.edu December 3rd, 2001 1 Abstract Indexing schemes in relational database have been well studied in the past, but this is not true in semi structured database and XML database. In this project, we designed and implemented novel indexing structures for XML data by extending the GiST software framework. In the ....

....third query is trying to search for a common ancestor of more than two entities. All of them are very common in querying XML documents, thus an index structure to facilitate these will be very helpful in improving the performance of XML database. This report is organized as follows. In Section 3, we present the related work. Design and implementation details are given in Section 4 and Section 5, respectively. In Section 6, we present the result and analy sis of the common ancestor index extension. Future work is discussed in Section 7, and we finally conclude in Section 8. 3 Related ....

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Elias Koutsoupias and D. S. Taylor. Tight Bounds for 2-Dimensional Indexing Schemes. Proceedings of the seventeenth ACM SIGACTSIGMOD -SIGART symposium on Principles of database systems, page 52-58. June 1998, Seattle, WA USA.

....for the two dimensional case. Unfortunately, their published proof is seriously flawed. Hellerstein, Koutsoupias and Papadimitriou [HKP97] introduced the indexability model, and published the first lower bounds, for restricted cases of two dimensional search. Subsequently, Koutsoupias and Taylor [KT98, KT99] provided lower bounds for orthogonal range search, but within a simplified complexity framework, where the e#ect of the block size is not accounted for. Samoladas and Miranker [SM98] introduced a general framework for lower bounds, and proved tight bounds for restricted d dimensional ....

....where the e#ect of the block size is not accounted for. Samoladas and Miranker [SM98] introduced a general framework for lower bounds, and proved tight bounds for restricted d dimensional range search problems. Arge, Samoladas and Vitter [ASV99] combined this technique with the results of [KT98] and provided strong lower bounds for two dimensional search, along with lower bounds on the space I O trade o#. These results have been obtained in the context of the indexability memory model. Extended discussion of this work can be found in Ch. 5 of this dissertation. 2.1.9 Persistence ....

E. Koutsoupias and David S. Taylor. Tight bounds for 2dimensional indexing schemes. In Proc. ACM Symp. Principles of Database Systems, pages 52--58, 1998.

....theory the focus is on bounding the number of disk blocks containing the answers to a query (access overhead) given a bound on the number of blocks used to store the data points (re dundancy) The search cost of computing which blocks to access is ignored. We generalize the results in [26, 14] and show a lower bound on redundancy for a given access overhead for the general 4 sided problem. We then show that this bound is tight by constructing an indexing scheme with a matching tradeoff between redundancy and access overhead. The indexing scheme is based upon an indexing scheme for the ....

....The access overhead A is defined as the least number such that every query q 2 Q is covered by at most A Sigma jqj=B Upsilon blocks of S , where jqj denotes the number of points that satisfy query q. The reader is referred to [10, 24] for a more detailed presentation. Koutsoupias and Taylor [14] applied indexability to two dimensional range searching and showed that a particular workload, the Fibonacci workload, seems to be worst case for two dimensional range queries. Using this result, they showed logarithmic upper and lower bounds on the redundancy for range search indexability. In ....

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E. Koutsoupias and D. S. Taylor. Tight bounds for 2dimensional indexing schemes. In Proc. ACM Symp. Principles of Database Systems, 1998.

....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 ....

E. Koutsoupias and D. S. Taylor. Tight bounds for 2-dimensional indexing schemes. In Proc. ACM Symp. Principles of Database Systems, pages 52--58, 1998.

....to index a given data set is practical for a given set of queries. Previous work on indexing data structures concentrated on the study of specialized problems. The first problem independent insight on external data structures was offered in [7] Continuing on this work, Koutsoupias and Taylor [10] investigate the indexability of 2 dimensional data sets, and derive asymptotically tight indexing schemes for these sets. In particular, they identify the Fibonacci workload as a worst case workload for 2 dimensional indexing. The research into external data structures has largely been ....

....is a lower bound by Subramanian and Ramaswamy [16] of Omega i N B log N log log B N j , for query I O cost bounded by O Gamma log c B N jQj B Delta . Although stronger than that of theorem 7.1, even this is not tight. Elsewhere in these proceedings, Koutsoupias and Taylor [10] show that logarithmic redundancy r = Omega Gamma416 N) is needed, if the access overhead is to be A B. Also, slightly higher redundancy r = 4 log(N=B) is sufficient for A 4, for any 2 dimensional workload. Thus, the trade off for 2 dimensional workloads exhibits threshold behaviour. These ....

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E. Koutsoupias and David S. Taylor. Tight bounds for 2-dimensional indexing schemes. In Proceedings of Symposium on Principles of Database Systems (PODS), 1998.

....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 d dimensional range queries, and derive a lower bound Omega Gamma logB log ff ) for the storage redundancy. Range queries are also considered in [52, 60]. Another interesting family of workloads is derived by the set inclusion queries. For some m 1, the domain D is the set of all possible subsets of the set f1; 2; mg. The instance I is a subset of D. Given a set S 2 D, we define a query as Q S = fX 2 I : X Sg, that is, all the sets in I ....

E. Koutsoupias and D. S. Taylor. Tight bounds for 2-dimensional indexing schemes. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 52--58, 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 ....

Elias Koutsoupias and David Scot Taylor. Tight bounds for 2-dimensional Indexing Schemes. In Proc. 17th ACM PODS Symposium on Principles of Database Systems, Seattle, 1998.

.... 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 arbitrary Euclidean points (as opposed to regular grid points) In particular, the Fibonacci workload of n points the regular 2 dimensional grid rotated by the golden ratio was analyzed. It was shown that there exists a constant c B , such that any ....

....simple, we treat the block size B as a constant, so, for example, the expression O(n) may conceal some multiplicative factor that depends on B and d. Our aim is to show the dependency of the indexing trade off on the workload size, not the block size. Our results We continue the work of [6] by extending it in two directions. We prove that logarithmic trade off is not a property of only structured workloads such as the Fibonacci workload, but it is a property of the vast majority of 2dimensional workloads: with high probability, a random 2 dimensional workload will require ....

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E. Koutsoupias and D. S. Taylor. Tight bounds for 2-dimensional indexing schemes In Proc. 17th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 52--58, Seattle, June 1998.

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