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Canonical form for graphs in quasipolynomial time: preliminary report

Published: 23 June 2019 Publication History

Abstract

We outline how to turn the author's quasipolynomial-time graph isomorphism test into a construction of a canonical form within the same time bound. The proof involves a nontrivial modification of the central symmetry-breaking tool, the construction of a canonical relational structure of logarithmic arity on the ideal domain based on local certificates.

References

[1]
{Ba79} László Babai: Monte Carlo algorithms in graph isomorphism testing. Université de Montréal Tech. Rep. DMS 79-10, 1979 (pp. 42). Accessible at http://people.cs.uchicago.edu/ ∼laci/lasvegas79.pdf {Ba15+} László Babai: Graph isomorphism in quasipolynomial time. arXiv:1512.03547, 2015–2019.
[2]
{BaCP82} László Babai, Peter J. Cameron, Péter P. Pálfy: On the orders of primitive groups with restricted nonabelian composition factors. J. Algebra 79 (1982), 161-168. {BaKL} László Babai, Paul Klingsberg, Eugene M. Luks: Canonical labelling for vertex coloured graphs. Unpublished, 1980.
[3]
{BaL83} László Babai and Eugene M. Luks: Canonical labeling of graphs. In: Proc. 15th STOC, ACM 1983, pp. 171–183. {Cam81} Peter J. Cameron: Finite permutation groups and finite simple groups, Bull. London Math Soc. 13 (1981) 1–22. {DiM96} John D. Dixon, Brian Mortimer: Permutation Groups. Springer Grad. Texts in Math. vol. 163, 1996
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{FG11} Lance Fortnow and Joshua A. Grochow: Complexity classes of equivalence problems revisited. Information and Computation 209 (2011) 748–763.
[5]
{FHL80} Merrick Furst, John Hopcroft, Eugene Luks: Polynomial-time algorithms for permutation groups. In: Proc. 21st IEEE FOCS, 1980, pp. 36–41.

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  1. Canonical form for graphs in quasipolynomial time: preliminary report

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    cover image ACM Conferences
    STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
    June 2019
    1258 pages
    ISBN:9781450367059
    DOI:10.1145/3313276
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    Published: 23 June 2019

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    Author Tags

    1. algorithms
    2. canonical form
    3. complexity
    4. graphs
    5. group theory
    6. isomorphism

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    • (2024)Canonical Forms for Matrix Tuples in Polynomial Time2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00054(780-789)Online publication date: 27-Oct-2024
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