Polynomial Time Algorithm for Graph Isomorphism Testing?

I just came across the following new report: http://arxiv.org/find/cs/1/au:+Trofimov_M/0/1/0/all/0/1.
The complexity of the graph isomoprphism problem is a longstanding open problem. Therefore, it will be interesting to check if the problem has finally been resolved.

Comments

Mark Reitblatt said…
It seems very unlikely. The paper is poorly organized, almost unreadable, and far from rigorous. For example, his algorithm seems to rest on computing what he calls a "W-Matrix", the definition of which is inscrutable. Then he doesn't show how to compute this matrix and instead argues about the complexity of computation based solely on the size of the matrix (clearly a lower bound). He also assumes arbitrarily sized real numbers and arbitrary precision real arithmetic without any argument about the complexity of this for his needs.
April 14, 2010 at 1:19 PM
Haris said…
My first impression was also *not convinced* but it was based on a very brief scan of the paper.
April 14, 2010 at 5:47 PM
Unknown said…
It's not solved: reading the first paragraph of section 2: WOLOG "undirected, connected graphs without loops". That means trees; the tree isomorphism problem is O(nlogn).
April 15, 2010 at 4:28 AM
Mark Reitblatt said…
I assume that "without loops" means "without self-loops" rather than "without cycles".
April 18, 2010 at 7:07 AM
Haris said…
Another claim:-)

http://arxiv.org/abs/1004.3702
April 22, 2010 at 9:27 PM
MT2 said…
W-Matrix definition is quite clear: see Definition 3. If you are interested in computing of W-Matrix, you can download source code: see Section 6. The main effort (to estimate complexity) is not the matrix, but solving the system (1). Loop is "edge from vertex a to vertex a", it is not cycle.
Thank you, MT.
April 24, 2010 at 8:00 PM
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