The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: how to extract the structure....
Replies: 1   Last Post: Mar 24, 2013 2:24 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
James Waldby

Posts: 545
Registered: 1/27/11
Re: how to extract the structure....
Posted: Mar 24, 2013 2:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sat, 23 Mar 2013 11:22:57 -0700, Dieter von Holten wrote:
> lets assume i have a set of lists (4 letter words...), like below:

> (1) abcd, aabb, abda, dbdb, bbca, afah, ...
> when i swap two letters, like a<->b, i get another set of lists:
> (2) bacd, bbaa, badb, dada, aacb, bfbh, ...
> or, by swapping a<->c in (1):
> (3) cbad, ccbb, cbdc, dbdb, bbac, cfch, ...
> the lists look different, but they share the same structure
> (4) 1234, 1122, 1241, 4242, 2231, 1516, ...

...[snip other examples]...
> the letters have no (implicit) value, they are just different symbols.
> any ideas ? what shall i google?

It might be that this problem can be put into correspondence
with the Graph isomorphism problem, whose complexity of solving
is not known, but is an important open question. See

Or, this problem might be easier for average cases. I didn't
understand examples 5 and 6 (snipped for brevity) but suppose
the word lists were related by word-reordering and simple
alphabetic substitution. If so, testing for isomorphism probably
can be done quickly by canonicalizing each word list. Eg,
replace the most common character by 1, the next most common
by 2, etc. When a tie occurs, break it by finding the most
common first character, or if that ties, the most common 2nd
character, or most common in the next combination of columns
to be considered, etc. As characters are named in this way,
remove them from future counting. This approach serves to
canonicalize examples 1-4 but presumably there are examples
it doesn't work for.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.