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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1998: STACS 98 pp 172–182Cite as

The complexity of modular graph automorphism

  • Complexity II
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

Abstract

Motivated by the question of the relative complexities of the Graph Isomorphism and the Graph Automorphism problems, we define and study the modular graph automorphism problems. These are the decision problems ModkGA which consist, for each k > 1, of deciding whether the number of automorphisms of a graph is divisible by k. The ModkGA problems all turn out to be intermediate in difficulty between Graph Automorphism and Graph Isomorphism. We define an appropriate search version of ModkGA and design an algorithm that polynomial-time reduces the ModkGA search problem to the decision problem. Combining this algorithm with an IP protocol, we obtain a randomized polynomial-time checker for ModkGA, for all k > 1.

Supported in part by NSF grants CCR-8958528 and CCR-9415410, and NASA grant NAG 52895. Work done while on sabbatical from Yale University and affiliated with the Human-Computer Interaction Laboratory.

Supported in part by the E.U. through ESPRIT project (no. LTR 20244, ALCOMIT) and by DGICYT (Koala project, with no. PB95-0787), and CICYT (no. TIC971475-CE). Work completed while visiting the first author at the Institute of Mathematical Sciences.

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References

  1. J. Balcázar, J. Diaz, and J. Gabarró. Structural Complexity II. Springer-Verlag, 1990.

    Google Scholar 

  2. J. Balcázar, J. Diaz, and J. Gabarró. Structural Complexity I. Springer-Verlag, second edition, 1995.

    Google Scholar 

  3. R. Beigel, M. Kummer, and F. Stephan. Approximable sets, Information and Computation 120(2):304–314, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Blum and S. Kannan. Designing programs that check their work, Journal of the ACM, 43:269–291, 1995.

    Article  Google Scholar 

  5. M. Blum, M. M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems, J. Comput. Syst. Sci. 47:73–83, 1993.

    MathSciNet  Google Scholar 

  6. R. Chang. On the structure of NP computations under boolean operators. Ph. D. Thesis, Cornell University, 1991.

    Google Scholar 

  7. S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM Journal on Computing 18:186–208, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Harary. Graph Theory, Addison Wesley, Reading, 1969.

    Google Scholar 

  9. J. Köbler, U. Schöning, and J. Torán. The graph isomorphism problem: its structural complexity, Birkhäuser, Boston, 1993.

    MATH  Google Scholar 

  10. A. Lozano and J. Tor\(\hat a\)n. On the nonuniform complexity of the graph isomorphism problem. In Proceedings of the 7th Structure in Complexity Theory Conference, pp. 118–129, 1992.

    Google Scholar 

  11. R. Mathon. A note on the graph isomorphism counting problem. Information Processing Letters, 8:131–132, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. P. Schnorr. On self-transformable combinatorial problems. Math. Programming Study, 14:95–103, 1982.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, 600113, Chennai, India

    V. Arvind

  2. Department of EE&CS, Lehigh University, 18015-3084, Bethlehem, PA, USA

    R. Beigel

  3. Universitat Politècnica de Catalunya, 08034, Barcelona, Catalonia, E.U.

    A. Lozano

Authors
  1. V. Arvind
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  2. R. Beigel
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  3. A. Lozano
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Editor information

Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Arvind, V., Beigel, R., Lozano, A. (1998). The complexity of modular graph automorphism. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028559

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  • DOI: https://doi.org/10.1007/BFb0028559

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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