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Symposium on Mathematical Fundamentals of Database Systems

MFDBS 1991: MFDBS 91 pp 146–159Cite as

A direct algorithm for computing the transitive closure of a two-dimensionally structured file

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 495))

Abstract

It is well-known that the computation cost to find the transitive closure (TC) of a graph stored as an adjacency matrix is the same, to within a constant factor, as matrix multiplication. In this paper, we present a new TC algorithm based on double hashing and two-dimensionally organized files. We show that, when using this algorithm, the computation and i/o costs of finding the TC of a database relation is like that of performing a relational composition operation. For sparse closures, sparse compositions will be performed, which may be significantly more thrifty than the corresponding matrix operations, which must be at least O(n 2), and for which most algorithms are O(n 3).

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Author information

Authors and Affiliations

  1. Data General Corporation, 01531, Westboro, MA

    Stephen Taylor

  2. Data/Knowledge Base Research Group Computer Science Department, Worcester Polytechnic Institute, 01609, Worcester, MA

    Nabil I. Hachem

Authors
  1. Stephen Taylor
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  2. Nabil I. Hachem
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Editor information

Bernhard Thalheim János Demetrovics H. -D. Gerhardt

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© 1991 Springer-Verlag Berlin Heidelberg

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Taylor, S., Hachem, N.I. (1991). A direct algorithm for computing the transitive closure of a two-dimensionally structured file. In: Thalheim, B., Demetrovics, J., Gerhardt, H.D. (eds) MFDBS 91. MFDBS 1991. Lecture Notes in Computer Science, vol 495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54009-1_11

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  • DOI: https://doi.org/10.1007/3-540-54009-1_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54009-0

  • Online ISBN: 978-3-540-47348-0

  • eBook Packages: Springer Book Archive

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