26 Apr 2000 02:34:48 -0400

Related articles |
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On CFL equivalence and graph isomorphism johnston.p@worldnet.att.net (Paul Johnston) (2000-04-20) |

Re: On CFL equivalence and graph isomorphism lex@cc.gatech.edu (2000-04-25) |

Re: On CFL equivalence and graph isomorphism colohan+@cs.cmu.edu (Christopher Brian Colohan) (2000-04-25) |

Re: On CFL equivalence and graph isomorphism pmoisset@altavista.net (Pablo) (2000-04-25) |

Re: On CFL equivalence and graph isomorphism ger@informatik.uni-bremen.de (George Russell) (2000-04-26) |

Re: On CFL equivalence and graph isomorphism bdm@cs.anu.edu.au (2000-04-26) |

Re: On CFL equivalence and graph isomorphism dmolnar@fas.harvard.edu (David A Molnar) (2000-04-27) |

Re: On CFL equivalence and graph isomorphism miyazaki@symbolix.cs.uoregon.edu (2000-04-27) |

From: | George Russell <ger@informatik.uni-bremen.de> |

Newsgroups: | comp.theory,comp.compilers |

Date: | 26 Apr 2000 02:34:48 -0400 |

Organization: | Universitaet Bremen, Germany |

Distribution: | inet |

References: | 00-04-140 00-04-167 |

Keywords: | parse, theory |

Christopher Brian Colohan wrote:

*>*

*> "Paul Johnston" <johnston.p@worldnet.att.net> writes:*

*>*

*> > Furthermore, what is the state of solving the Graph Isomorhism*

*> > problem? Is there no hope?*

*>*

*> I believe it has been proven to be NP-complete (I need to check in my*

*> Gary&Johnson to be sure, and I am out of town...).*

Er I don't. Perhaps Christopher Colohan is confusing it with Subgraph

Isomorphism (which is indeed NP-complete). Graph Isomorphism doesn't

seem to be nearly as hard as that. I get the impression it's rather

like telling knots apart, in that there are quite a lot of

characteristics (degree sequences and generalisations thereof,

eigenvalues and angles with eigenvectors . . .) which will distinguish

virtually all pairs of graphs quickly, but all known polynomial

methods so far fail to distinguish a few irritating cases. But I'm

somewhat out of date; for all I know someone has a polynomial

algorithm now. I don't think it is unlikely that a polynomial

algorithm will be discovered some time in the future, or it might be

(as I think G&J suggests) that this is one of a class of problems

which are just a little bit worse than "P" but not anything like

"NP-complete".

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