Newsgroups: comp.constraints
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From: leconte@ilog.ilog.fr (Michel Leconte)
Subject: Re: Question: constraint terminology
Message-ID: <1995Jul3.124452.21746@ilog.fr>
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References:  <80452307113n12@137.224.11.42>
Date: Mon, 3 Jul 95 12:44:52 GMT
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In article <80452307113n12@137.224.11.42>, Peter=Schotman%Users%INFO.WAU@Vines.WAU.NL writes:
|> Dear Netters,
|>[...deleted...] 
|>
|> Question: Could somebody explain the following terms:
|> 
|> - Global constraints
|> (the FAQ says: "constraints with maximum 
|> arity", does that mean that if the problem contains N variables only 
|> N-ary constraints are considered global?)
The term "global constraint" is related with the level of consistency achieved
by the propagation engine. A clssical example is the "alldiff" constraint:
   alldiff(x1,...xi,...xn)
setting that, in any solution, all the values of the xi must be pairwise distinct.
The traditionnal (local) handling of this constraint ensures that, each time 
a variable is instanciated to a value, this value does not appear in the
domains of the other variables.
More formally, the following stands:
     forall xi, forall xj != xi, forall u belonging to the domain of xi,
     there exists a value v in the domain of xj such that u != v.
The global handling of this constraint should maintain the following
property:
     forall xi, forall u in the domain of xi,there exist values 
     from domains of {x1,...,xj,...xn | xj != xi} such that u and these
     values are pairwise distinct.
In other word, the global consistency of a constraint is: any value in 
the domain of a variable belongs to a solution.
The global consistency of the alldiff constraint has been shown by J-C Regin
in: "A filtering algorithm for constraint of difference in CSPs. Jean-Charles
Regin, AAAI 94, Seattle, Wsashington".

|> 
|> - Specific and structural constraints 
|> (in: CHIC lessons on CLP methodology, ECRC-report)
|> A lot of applications (I think) contain both a set of reasonably stable 
|> (permament) constraints as well as constraints that change from 
|> problem to problem instance, is that what is ment here?
|> 
The CHIC project (Constraint Handling in Industry and Commerce, Esprit project
number 5291) was finished at the end of 1994. One of its result concerns the
CLP methodology, with a big emphasis on the qualification phase: given a 
(instance of a) problem, (try to) predict if:
   - it is feasible,
   - it needs the coding of new constraints (e.g. the cooperation
     of OR algorithms and propagations).
One of the first phase of the methodology is to differentiate specific and
structural constraints:
Structural constraints deals with global properties of the problem and act
on variables playing similar roles (the sub-problem is homogeneous).
For example, you can easily encode a flow transportation problem in a CLP
using elementary arithmetic constraint. Netherless, there is a more global
structure (a graph) that represents the problem together with a _structural_
constraint (flow conservation) to express it.
At the opposite, specific constraints depends on the instance of the 
application.

|> 
|> Also I would appriciate pointers to papers that explicitly deal with 
|> problem solving systems for a combination of continuous and symbolic 
|> constraints.

You could have a look at "H. Berinbger and B. De Backer. Combinatorial
Problem Solving in Constraint Logic Programming with cooperating
Solvers. In C. Beierle and L. Plumers Editors, Logic Programming:
Formal methods and Practical Applications, Elsevier Science B.V. 1995"

|> 
|> Thanks in advance, 
|> 
|> Peter Schotman
|> 

Michel Leconte 


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