Corpus ID: 12703138

Bidirectional Collision Detection and Faster Deterministic Isomorphism Testing

@article{Rosenbaum2013BidirectionalCD,
  title={Bidirectional Collision Detection and Faster Deterministic Isomorphism Testing},
  author={David J. Rosenbaum},
  journal={ArXiv},
  year={2013},
  volume={abs/1304.3935}
}
In this work, we introduce bidirectional collision detection --- a new algorithmic tool that applies to the collision problems that arise in many isomorphism problems. For the group isomorphism problem, we show that bidirectional collision detection yields a deterministic n^((1 / 2) log n + O(1)) time algorithm whereas previously the n^(log n + O(1)) generator-enumeration algorithm was the best result for several decades. For the hard special case of solvable groups, we combine bidirectional… Expand
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  • 2017
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References

SHOWING 1-10 OF 21 REFERENCES
Testing isomorphism of combinatorial and algebraic structures
  • 14
Code equivalence and group isomorphism
  • 46
  • PDF
Breaking the nlog n Barrier for Solvable-Group Isomorphism
  • 15
  • PDF
Linear time algorithms for Abelian group isomorphism and related problems
  • T. Kavitha
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 2007
  • 34
Moderately Exponential Bound for Graph Isomorphism
  • L. Babai
  • Mathematics, Computer Science
  • FCT
  • 1981
  • 93
Polynomial-Time Isomorphism Test for Groups with No Abelian Normal Subgroups - (Extended Abstract)
  • 25
  • PDF
An O(n) Algorithm for Abelian p-Group Isomorphism and an O(n log n) Algorithm for Abelian Group Isomorphism
  • N. Vikas
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1996
  • 32
Polynomial-time Isomorphism Test for Groups with Abelian Sylow Towers
  • 22
  • PDF
Computational complexity and the classification of finite simple groups
  • L. Babai, W. Kantor, E. Luks
  • Mathematics, Computer Science
  • 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
  • 141
  • Highly Influential
  • PDF
Efficient Isomorphism Testing for a Class of Group Extensions
  • F. Gall
  • Mathematics, Computer Science
  • STACS
  • 2009
  • 23
  • PDF
...
1
2
3
...