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The Dynamic Complexity of Transitive Closure Is in DynTC°

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Database Theory — ICDT 2001 (ICDT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1973))

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Abstract

This paper presents a fully dynamic algorithm for maintaining the transitive closure of a directed graph. All updates and queries can be computed by constant depth threshold circuits of polynomial size (TC° circuits). This places transitive closure in the dynamic complexity class DynTC°, and implies that transitive closure can be maintained in databases using updates written in a first order query language plus counting operators, while keeping the size of the database polynomial in the size of the graph.

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References

  1. Barrington, Immerman, and Straubing. On uniformity within NC 1. In SCT: Annual Conference on Structure in Complexity Theory, 1988.

    Google Scholar 

  2. Paul W. Beame, Stephen A. Cook, and H. James Hoover. Log depth circuits for division and related problems. SIAM Journal on Computing, 15(4):994–1003, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Dong, L. Libkin, and L. Wong. On impossibility of decremental recomputation of recursive queries in relational calculus and SQL. In International Workshop on Database Programming Languages, 1995.

    Google Scholar 

  4. Guozhu Dong and Jianwen Su. Incremental and decremental evaluation of transitive closure by first-order queries. Information and Computation, 120(1):101–106, July 1995.

    Article  MATH  MathSciNet  Google Scholar 

  5. Jacob Holm, Kristian de Lichtenberg, and Mikkel Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge and biconnectivity. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC-98), pages 79–89, New York, May 23-26 1998. ACM Press.

    Google Scholar 

  6. Neil Immerman. Descriptive Complexity. Springer-Verlag, New York, 1999.

    MATH  Google Scholar 

  7. Neil Immerman and Susan Landau. The complexity of iterated multiplication. Information and Computation, 116(1):103–116, January 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. Leonid Libkin and Limsoon Wong. Incremental recomputation of recursive queries with nested sets and aggregate functions. In Proc. of Database Programming Languages (DBPL’97), pages 222–238, Estes Park, CO, 1998. Springer-Verlag, Lecture Notes in Computer Science 1369.

    Google Scholar 

  9. Sushant Patnaik and Neil Immerman. Dyn-FO: A parallel, dynamic complexity class. Journal of Computer and System Sciences, 55(2):199–209, October 1997.

    Article  MathSciNet  Google Scholar 

  10. John H. Reif and Stephen R. Tate. On threshold circuits and polynomial computation. SIAM Journal on Computing, 21(5):896–908, October 1992.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Massachusetts, MA 01002, Amherst

    William Hesse

Authors
  1. William Hesse
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Editor information

Editors and Affiliations

  1. Limburg University (LUC), 3590, Diepenbeek, Belgium

    Jan Van den Bussche

  2. Department of Computer Science and Engineering, University of California, 92093-0114, La Jolla, CA, USA

    Victor Vianu

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© 2001 Springer-Verlag Berlin Heidelberg

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Hesse, W. (2001). The Dynamic Complexity of Transitive Closure Is in DynTC°. In: Van den Bussche, J., Vianu, V. (eds) Database Theory — ICDT 2001. ICDT 2001. Lecture Notes in Computer Science, vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44503-X_16

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  • DOI: https://doi.org/10.1007/3-540-44503-X_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41456-8

  • Online ISBN: 978-3-540-44503-6

  • eBook Packages: Springer Book Archive

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