On rectangular partitionings in two dimensions: Algorithms, complexity, and applications

S. Muthukrishnan, Viswanath Poosala, Torsten Suel

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Partitioning a multi-dimensional data set into rectangular partitions subject to certain constraints is an important problem that arises in many database applications, including histogram-based selectivity estimation, load-balancing, and construction of index structures. While provably optimal and efficient algorithms exist for partitioning one-dimensional data, the multi-dimensional problem has received less attention, except for a few special cases. As a result, the heuristic partitioning techniques that are used in practice are not well understood, and come with no guarantees on the quality of the solution. In this paper, we present algorithmic and complexity-theoretic results for the fundamental problem of partitioning a two-dimensional array into rectangular tiles of arbitrary size in a way that minimizes the number of tiles required to satisfy a given constraint. Our main results are approximation algorithms for several partitioning problems that provably approximate the optimal solutions within small constant factors, and that run in linear or close to linear time. We also establish the NP-hardness of several partitioning problems, therefore it is unlikely that there are efficient, i.e., polynomial time, algorithms for solving these problems exactly. We also discuss a few applications in which partitioning problems arise. One of the applications is the problem of constructing multi-dimensional histograms. Our results, for example, give an efficient algorithm to construct the V-Optimal histograms which are known to be the most ac- curate histograms in several selectivity estimation problems. Our algorithms are the first to provide guaranteed bounds on the quality of the solution.

    Original languageEnglish (US)
    Title of host publicationDatabase Theory - ICDT 1999 - 7th International Conference, Proceedings
    PublisherSpringer Verlag
    Pages236-256
    Number of pages21
    Volume1540
    ISBN (Print)3540654526, 9783540654520
    StatePublished - 1998
    Event7th International Conference on Database Theory, ICDT 1999 - Jerusalem, Israel
    Duration: Jan 10 1999Jan 12 1999

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume1540
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other7th International Conference on Database Theory, ICDT 1999
    CountryIsrael
    CityJerusalem
    Period1/10/991/12/99

    Fingerprint

    Algorithm Complexity
    Partitioning
    Two Dimensions
    Tile
    Histogram
    Approximation algorithms
    Selectivity
    Resource allocation
    Efficient Algorithms
    Hardness
    Polynomials
    NP-hardness
    Multidimensional Data
    Optimal Algorithm
    Load Balancing
    Polynomial-time Algorithm
    Linear Time
    Approximation Algorithms
    Optimal Solution
    Partition

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Muthukrishnan, S., Poosala, V., & Suel, T. (1998). On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. In Database Theory - ICDT 1999 - 7th International Conference, Proceedings (Vol. 1540, pp. 236-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1540). Springer Verlag.

    On rectangular partitionings in two dimensions : Algorithms, complexity, and applications. / Muthukrishnan, S.; Poosala, Viswanath; Suel, Torsten.

    Database Theory - ICDT 1999 - 7th International Conference, Proceedings. Vol. 1540 Springer Verlag, 1998. p. 236-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1540).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Muthukrishnan, S, Poosala, V & Suel, T 1998, On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. in Database Theory - ICDT 1999 - 7th International Conference, Proceedings. vol. 1540, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1540, Springer Verlag, pp. 236-256, 7th International Conference on Database Theory, ICDT 1999, Jerusalem, Israel, 1/10/99.
    Muthukrishnan S, Poosala V, Suel T. On rectangular partitionings in two dimensions: Algorithms, complexity, and applications. In Database Theory - ICDT 1999 - 7th International Conference, Proceedings. Vol. 1540. Springer Verlag. 1998. p. 236-256. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Muthukrishnan, S. ; Poosala, Viswanath ; Suel, Torsten. / On rectangular partitionings in two dimensions : Algorithms, complexity, and applications. Database Theory - ICDT 1999 - 7th International Conference, Proceedings. Vol. 1540 Springer Verlag, 1998. pp. 236-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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