S. Muthukrishnan, V. Poosala and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity and applications. Proc. Intl Conf on Database Theory (ICDT), 1999, 236--256.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....statistical variance of the spatial densities of all points inside it. Since a small spatial skew indicates better uniformity, MinSkew aims at minimizing i=1 m (b i .numb i .skew) i.e. the weighted sum of the spatialskews of the buckets. Computing the optimal buckets, however, is NP hard [MPS99]. To reduce the computation cost, APR99] partitions the original space into a grid with HH regular cells (where H is the resolution) and associate each cell c with (i) the number c.num of objects whose centroids fall in c.MBR, ii) the average extent length c.len of objects satisfying (i) and ....

Muthukrishnan, S., Poosala, V., Suel, T. On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications. ICDT, 1999.

....class of problems for which we can have near optimal data stream algorithms. 1. INTRODUCTION Histograms capture distribution statistics in a space ef cient fashion. They have been designed to work well for numeric value domains, and have long been used to support cost based query optimization [22, 11, 12, 25, 27, 26, 23, 14, 13, 15, 20, 17], approximate query answering [7, 2, 1, 29, 28, 24] data mining [16] and map simpli cation [3] Query optimization is a problem of central interest to database systems. A database query is translated by a parser into a tree of physical database operators (denoting the dependencies between ....

..... 5.00. erators of interest exist, the most common being select and join operators. A select operator commonly corresponds to an equality or a range predicate that has to be executed on the database and various works deal with the construction of good histograms for such operations [22, 11, 23, 15, 13, 20, 17]. The result of such estimation through the use of a histogram represents the approximate number of database tuples satisfying the predicate (commonly referred to as a selectivity estimate) and can determine whether a database index should be used (or constructed) to execute this operator. Join ....

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S. Muthukrishnan, V. Poosala, and T. Suel. On Rectangular Partitioning In Two Dimensions: Algorithms, Complexity and Applications. Proceedings of ICDT, 1999.

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S. Muthukrishnan, V. Poosala and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity and applications. Proc. Intl Conf on Database Theory (ICDT), 1999, 236--256.

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S. Muthukrishnan, V. Poosala and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity and applications. Proc. Intl Conf on Database Theory (ICDT), 1999, 236--256.

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S. Muthukrishnan, V. Poosala and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity and applications. In Proc. of the Int. Conf. on Database Theory, pages 236--256, 1999.

....SUM VAR metric in Example 2. We also extend the known result for the MAX SUM metric in Example 1 [7, 10] that it is NP Complete to compute a partitioning with a value less than two times the optimum to several new metrics. A preliminary version of the results in this paper appeared as part of [26]. Our algorithms are based on the framework of Bronnimann and Goodrich in [5] and exploit an interesting relationship between partitioning problems and the construction of small nets. In particular, the partitioning problem for the MAX SUM metric can be reduced to a Set Cover problem with ....

S. Muthukrishnan, V. Poosala and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity and applications. In Proc. of the Int. Conf. on Database Theory, pages 236--256, 1999.

....ffl on the data cube error E (Definition 3) the ffl optimal configuration is the configuration that requires the least amount of space while resulting in an error of at most ffl. Earlier research on optimization problems similar in nature to this problem has shown many of them to be NP Hard [13, 7]. Though the complexity of our specific problem has not yet been established, there is a strong likelihood that it may not have an efficient solution. However, we have shown in [16] that the identification of the ffl optimal configuration is upper bounded by the minimum weighted set cover problem ....

S. Muthukrishnan, V. Poosala, and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. 7th International Conference on Database Theory, January, 1999.

....configuration that uses the least space such that none of the sub cube errors exceeds 0:5. Next, we present theorems and algorithms for identifying the ffl optimal configurations. Earlier research on optimization problems similar in nature to this problem has shown many of them to be NP Hard [17, 9]. Though the complexity of our specific problem has not yet been established, there is a strong likelihood that it may not have an efficient solution. Hence, we have developed the following efficient heuristic algorithm that generates a solution within a factor of the optimal configuration. ....

S. Muthukrishnan, V. Poosala, and T. Suel. On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. 7th International Conference on Database Theory, January, 1999.

....heft is beyond certain prune condition. There is no efficient pruning strategy without rounding, since there are many large tiles that cannot be pruned. We have different pruning conditions for MAX and SUM. Due to space constraints, we omit the description of these conditions which can be found in [29]. Two examples of the results we obtain for MAX metrics are: an O(N 1:25 (B ) 3 ) time algorithm for factor 9 approximation, and O(N(B ) 3 ) time algorithm for factor 25 approximation. Further results for MAX, SUM and other superadditive metrics can be found in [29] 5 Arbitrary ....

....which can be found in [29] Two examples of the results we obtain for MAX metrics are: an O(N 1:25 (B ) 3 ) time algorithm for factor 9 approximation, and O(N(B ) 3 ) time algorithm for factor 25 approximation. Further results for MAX, SUM and other superadditive metrics can be found in [29]. 5 Arbitrary Partitionings 5.1 NP Hardness Results In this subsection, we prove NP hardness results for several metrics that show that minimizing the partitioning with p tiles that minimizes the heft is NP hard. In fact, the proof also implies limits on the approximability of the problem for ....

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S. Muthukrishnan, V. Poosala and T. Suel. On rectangular partitionings in two dimensions: algorithms, complexity and applications. Manuscript, 1998.

....well using histograms in a small amount of space. estimation problems that have been studied extensively in the database literature. Most previous works have focused on approximating the distributions of single numerical attributes. Even the ones studying multidimensional data [PI97, MPS99] have concentrated on approximating the frequencies of points in space. Many of these techniques are aimed at data with highly skewed frequencies. However, they do not perform as well when the frequency domain is relatively uniform but the value domain (i.e. placement of points in space) is ....

....clear that a partitioning with small spatial skew is likely to be highly accurate in approximating the given data. Unfortunately, building optimal partitionings, which minimize the spatial skew using a given amount of space, is a difficult problem that is provably NPhard for even simple instances [MPS99, KMS97] One technique for reducing the complexity of constructing good partitionings is to restrict ourselves to binary space partitionings (BSP) The partitioning of a region is said to be a BSP if we can find a vertical or horizontal line that divides the input region into two sub regions such ....

[Article contains additional citation context not shown here]

S. Muthukrishnan, Viswanath Poosala, and Torsten Suel. On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. 7th International Conference on Database Theory, January, 1999.

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Muthukrishnan, S., Poosala, V., Suel, T., On Rectangular Partitioning in Two Dimensions: Algorithms, Complexity and Applications, Proc. ICDT 1999, Jerusalem, Israel.

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Muthukrishnan S., Poosala V., Suel T.: On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications. ICDT (1999) 236-256

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S. Muthukrishnan, V. Poosala and T. Suel. "On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity and Applications", in Procs. of the International Conference on Database Theory, Jerusalem, 1999.

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