Dear George,
you may want to take a look at finite set constraints and how they are
related to finite domain constraints. There is a finite set constraint
tutorial..
Best,
Torsten
On 25.08.2006, at 21:06, George Rudolph wrote:
I have been working on the following problem from Combinatorial Design
Theory – working toward a Finite Domain Constraint Solution rather
than a generate-and-test solution.
given a set of points {0, 1, 2, ..., 92}, find a set of 2,139
unordered triples (blocks) such that each point x appears in 69
blocks--twice in blocks with 46 of the Points and once in blocks with
the other 46--and that no two triples are equal.
Taking advantage of various symmetries, I can reduce the problem from
looking for 2,196 blocks to looking for 23 blocks, because each one
of the 23 generates 91 others.
One way to proceed is to compute the differences between elements
within each block (so one block generates 6 differences), and count
the differences generated by all the blocks. The goal is to find sets
of 23 triples such that when the differences are computed, half the
differences appear once, and half appear twice. , and none can be 0.
So far, I have modeled the problem as a set of 23 triples, where each
element of a triple is a Finite Integer Domain, and I have a way to
constrain the triples so that no two triples are equal. What I need
help with is this:
How do I specify the difference constraints?
How do I specify cardinality constraints on the set of differences
without doing some kind of brute-force count?
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Torsten Anders
Sonic Arts Research Centre • Queen's University Belfast
Frankstr. 49 • D-50996 Köln
Tel: +49-221-3980750
http://www.torsten-anders.de
http://strasheela.sourceforge.net
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