Asymptotically optimal declustering schemes for 2-dim range queries

Sinha, Rakesh Kumar; Bhatia, Randeep; Chen, Chung‐Min

doi:10.1016/s0304-3975(02)00742-9

Cited by 8 publications

(18 citation statements)

References 18 publications

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“…This last argument increases the implicit constant of the lower bound by a factor of 3 d 2d compared to the approach of Sinha et al [SBC03]. We briefly show how to use the above to prove the Ω(log M) bound for dimension d = 2.…”

Section: The Lower Boundmentioning

confidence: 80%

“…Anstee et al [ADKS00] only treated latin square type colorings of [M] 2 and posed it an open problem to extend their result to arbitrary colorings. The proof in [SBC03] does not have this restriction, but is not very precise, which in particular helped to hide the error for d > 2.…”

Section: The Lower Boundmentioning

confidence: 99%

“…Round R to a boxR with corners in {0, 1 M , · · · , M −1 M , 1} d in such a way that R ∩ P =R ∩ P. Then R andR have similar volume and hence similar discrepancy. RescalingR yields a hyperedgeR with combinatorial discrepancy equal to the geometric one ofR.The small, but crucial mistake in the proof of Sinha et al[SBC03] is hidden in the transfer from the geometric discrepancy setting back to the combinatorial one. Unlike in dimension d = 2, rounding R toR does not yield a constant change in the discrepancy in higher dimensions.…”

mentioning

confidence: 97%

“…The general idea in the proofs of the lower bound for declustering schemes in Sinha et al[SBC03] and Anstee et al[ADKS00] (for d = 2 only) is the following.Any low-discrepancy M-coloring of [M] d has color classes of approximately M d−1 vertices. By scaling, such a color class yields an M d−1 -point set P in [0, 1) d .…”

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confidence: 99%

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Improved bounds and schemes for the declustering problem

Doerr

Hebbinghaus

Werth

2006

Theoretical Computer Science

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The declustering problem is to allocate given data on parallel working storage devices in such a manner that typical requests find their data evenly distributed on the devices. Using deep results from discrepancy theory, we improve previous work of several authors concerning range queries to higher-dimensional data. We give a declustering scheme with an additive error of O d (log d−1 M ) independent of the data size, where d is the dimension, M the number of storage devices and d − 1 does not exceed the smallest prime power in the canonical decomposition of M into prime powers. In particular, our schemes work for arbitrary M in dimensions two and three. For general d, they work for all M ≥ d − 1 that are powers of two. Concerning lower bounds, we show that a recent proof of a Ω d (log d−1 2 M ) bound contains an error. We close the gap in the proof and thus establish the bound. * supported by the DFG-Graduiertenkolleg 357 "Effiziente Algorithmen und

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Section: The Lower Boundmentioning

confidence: 80%

Section: The Lower Boundmentioning

confidence: 99%

mentioning

confidence: 97%

mentioning

confidence: 99%

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Improved bounds and schemes for the declustering problem

Doerr

Hebbinghaus

Werth

2006

Theoretical Computer Science

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“…Various declustering schemes have been proposed for range queries, including those that are specifically devised for uniform data [13], [19], [14], [33], [29], [30], [21], [16], [6], [7], [2], [31], and those that work for both uniform and nonuniform data [15], [23], [27], [5].…”

Section: Introductionmentioning

confidence: 99%

Multidimensional declustering schemes using Golden Ratio and Kronecker Sequences

Chen¹,

Bhatia²,

Sinha

2003

IEEE Trans. Knowl. Data Eng.

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We propose a new declustering scheme for allocating uniform multidimensional data among parallel disks. The scheme, aimed at reducing disk access time for range queries, is based on Golden Ratio Sequences for two dimensions and Kronecker Sequences for higher dimensions. Using exhaustive simulation, we show that, in two dimensions, the worst-case (additive) deviation of the scheme from the optimal response time for any range query is one when the number of disks (M) is at most 22; its worst-case deviation is two when M 94; and its worst-case deviation is four when M 550. In two dimensions, we prove that whenever M is a Fibonacci number, the average performance of the scheme is within 14 percent of the (generally, unachievable) strictly optimal scheme and its worst-case response time is within a multiplicative factor three of the optimal response time for any query, and within a factor 1:5 of the optimal for large queries. We also present comprehensive simulation results, on two-dimensional as well as on higherdimensional data, that compare and demonstrate the advantages of our scheme over some recently proposed schemes in the literature.

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