Improved Bounds for Finger Search on a RAM

Kaporis, Alexis C.; Makris, Christos; Sioutas, Spyros; Tsakalidis, Athanasios K.; Tsichlas, Kostas; Zaroliagis, Christos

doi:10.1007/978-3-540-39658-1_31

Cited by 30 publications

(20 citation statements)

References 17 publications

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“…The ISB-tree is a two-level data structure. The upper level is a non -straightforward externalization of the Static Interpolation Search Tree (SIST) presented in [11]. In the definition of the (f 1 , f 2 )-smooth densities [26,19],…”

Section: Preliminariesmentioning

confidence: 99%

“…The class of (f 1 , f 2 )-smooth distributions (for appropriate choices of f 1 and f 2 ) is a superset of both regular and uniform classes of distributions, as well as of several non-uniform classes [3,11]. Actually, any probability distribution is (f 1 , Θ(n))-smooth, for a suitable choice of β.…”

Section: Preliminariesmentioning

confidence: 99%

“…Let also μ 1 (·) random be the sequence of keys of super-block representatives. According to combinatorial game of bins and balls presented in [11], we store these keys in N = n 2 /lnn 2 buckets, each of which contains O(lnn 2 ) keys.…”

Section: Building Nefosmentioning

confidence: 99%

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NEFOS: Rapid Cache-Aware Range Query Processing with Probabilistic Guarantees

Sioutas

Tsichlas

Karydis

et al. 2011

Lecture Notes in Computer Science

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Abstract. We present NEFOS (NEsted FOrest of balanced treeS), a new cache-aware indexing scheme that supports insertions and deletions in O(1) worst-case block transfers for rebalancing operations (given and update position) and searching in O(log B log n) expected block transfers, (B= disk block size and n= number of stored elements). The expected search bound holds with high probability for any (unknown) realistic input distribution. Our expected search bound constitutes an improvement over the O(log B log n) expected bound for search achieved by the ISB-tree (Interpolation Search B-tree), since the latter holds with high probability for the class of smooth only input distributions. We define any unknown distribution as realistic if the smoothness doesn't appear in the whole data set, still it may appear locally in small spatial neighborhoods. This holds for a variety of real-life non-smooth distributions like skew, zipfian, powlaw, beta e.t.c.. The latter is also verified by an accompanying experimental study. Moreover, NEFOS is a B-parametrized concrete structure, which works for both I/O and RAM model, without any kind of transformation or adaptation. Also, it is the first time an expected sub-logarithmic bound for search operation was achieved for a broad family of non-smooth input distributions.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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NEFOS: Rapid Cache-Aware Range Query Processing with Probabilistic Guarantees

Sioutas

Tsichlas

Karydis

et al. 2011

Lecture Notes in Computer Science

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“…The class of (f1, f2)-smooth distributions (for appropriate choices of f1 and f2) is a superset of both regular and uniform classes of distributions, as well as of several non-uniform classes [1,17]. Actually, any probability distribution is (f1, Θ(n))-smooth, for a suitable choice of β.…”

Section: Probability Distributionsmentioning

confidence: 99%

“…Under this assumption, according to the combinatorial game of bins and balls, presented in Section 5 of [17], the size of every bucket is O(log c n), where c > 0 is a constant, and no bucket becomes empty w.h.p. We consider epochs of size O(log n), with respect to update operations.…”

Section: The Solution For Random Distri-butionsmentioning

confidence: 99%

Efficient processing of 3-sided range queries with probabilistic guarantees

Kaporis

Papadopoulos

Sioutas

et al. 2010

Proceedings of the 13th International Conference on Database Theory

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This work studies the problem of 2-dimensional searching for the 3-sided range query of the form [a, b] × (−∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3-sided queries in O(log n + t) worst case time and scales with O(log log n) expected with high probability update time, under continuous µ-random distributions of the x and y coordinates, where n is the current number of stored points and t is the size of the query output. Our expected update bound constitutes a considerable improvement over the O(log n) update time bound achieved by the classic Priority Search Tree of McCreight [23], as well as over the Fusion Priority Search Tree of Willard [30], which requires O( log n log log n ) time for all operations. Moreover, we externalize this solution, gaining O(log B n + t/B) worst case and O(logBlogn) amortized expected with high probability I/Os for query and update operations respectively, where B is the disk block size. Then, combining the Modified Priority Search Tree [27] with the Priority Search Tree [23], we achieve a query time of O(log log n + t) expected with high probability and an update time of O(log log n) expected with high probability, under the assumption that the x-coordinates are continuously drawn from a smooth distribution and the ycoordinates are continuously drawn from a more restricted class of distributions. The total space is linear. Finally, we externalize this solution, obtaining a dynamic data strucPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ICDT 2010, March 22-25, 2010, Lausanne, Switzerland. Copyright 2010 ture that answers 3-sided queries in O(log B log n + t/B) I/Os expected with high probability, and it can be updated in O(log B log n) I/Os amortized expected with high probability and consumes O(n/B) space, under the same assumptions.

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