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Generic case complexity of the Graph Isomorphism Problem

Generic case complexity of the Graph Isomorphism Problem Abstract The edge test is a partial algorithm for the Graph Isomorphism Problem based on comparison the number of edges. We perform a probabilistic analysis of the efficiency of the edge test. With the binomial distribution B ( n , p ) on the set of inputs, we estimate the asymptotic failure probability of the edge test depending on the rate of decay of parameter p . In particular, if p ≤ 1/2, n p → λ > 0, then the asymptotic failure probability is nonzero, so that the edge test does not solve generically the Graph Isomorphism Problem. On the other hand, if p ≤ 1/2, n p → ∞, then the failure set is negligible and the edge test generically solves the Graph Isomorphism Problem in polynomial time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Generic case complexity of the Graph Isomorphism Problem

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2016-0008
Publisher site
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Abstract

Abstract The edge test is a partial algorithm for the Graph Isomorphism Problem based on comparison the number of edges. We perform a probabilistic analysis of the efficiency of the edge test. With the binomial distribution B ( n , p ) on the set of inputs, we estimate the asymptotic failure probability of the edge test depending on the rate of decay of parameter p . In particular, if p ≤ 1/2, n p → λ > 0, then the asymptotic failure probability is nonzero, so that the edge test does not solve generically the Graph Isomorphism Problem. On the other hand, if p ≤ 1/2, n p → ∞, then the failure set is negligible and the edge test generically solves the Graph Isomorphism Problem in polynomial time.

Journal

Groups Complexity Cryptology – de Gruyter

Published: May 1, 2016

References

  • Almost every graph is vertex - oblique Discrete Almost every graph is vertex - obliqueDiscrete Math
    Schreyer
  • A personal view of average - case complexity Proceedings of the th Annual Structure in Complexity Theory Conference IEEE Press Piscateway A personal view of average - case complexityProceedings of the th Annual Structure in Complexity Theory ConferenceSCT
    Impagliazzo
  • Random graph isomorphism SIAM Random graph isomorphismSIAM
    Babai
  • Group - Theoretic Algorithms and Graph Isomorphism Lecture Notes in Comput Group - Theoretic Algorithms and Graph IsomorphismLecture Notes in Comput
    Hoffmann
  • Average - case Complexity Found Trends Theor Average - case ComplexityFound Trends Theor
    Bogdanov