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From: csc6bms@gps.leeds.ac.uk (B M Smith)
Subject: Re: exceptionally hard problems
Message-ID: <1994Sep8.145544.28108@leeds.ac.uk>
Sender: news@leeds.ac.uk
Organization: University of Leeds, England
Date: Thu, 8 Sep 1994 15:55:44 +0100 (BST)
References: <3473dh$27c@todd-06.cs.strath.ac.uk> <347ra0$jo9@peaches.cs.utexas.edu>
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I've just tried Pat's problem with fc-dvo and found the following solution in
7166 consistency checks:

2 2 2 2 1 1 1 4 1 1 
1 1 1 2 3 1 1 4 1 1
1 1 1 1 1 1 3 3 1 3 
1 1 1 3 8 4 2 1 1 1
1 1 7 6 1 2 2 3 1 2

The difference between my version of fc-dvo and Pat's may be in selecting the
first variable; I choose the variable involved in most constraints (in this
case, variable 19).

So I don't think that fc-dvo is an exceptionally bad algorithm; it just happened
that one version of it was particularly unlucky in this case.  (We all make
mistakes...)  What's maybe more interesting is why this particular problem has the
potential to cause such severe difficulties.  It's perhaps suggestive that both
my solution and Pat's solution, which are quite different, both have the value 7
for variable 43. It may be that for some reason this is the only possible value
for this variable, so that any algorithm that considers this variable early in
the search and considers its values in numerical order would have to do a
tremendous amount of work to find any solution.  (But if this is so, Pat's
experience suggests that it will take fc more than 710 million consistency checks
to prove it ...)

Barbara Smith
