Newsgroups: comp.constraints
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From: zeller@ips.cs.tu-bs.de (Andreas Zeller)
Subject: Solving a conjunction of X <= Y clauses
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Date: Mon, 9 Jan 1995 16:53:43 GMT
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I am looking for an efficient algorithm to solve the following problem.

Let n denote numerical constants, and x, y variables.  Let T be a
boolean conjunction of constraints where each constraint has one of
the forms

  1.  x OP n   with OP in { <, <=, =, >=, >, <> }
  2.  x OP y   with OP in { <, <=, =, >=, >, <> }

The problem is to find out whether T is satisfiable (i.e. there exists
a variable assignment such that all constraints are satisfied), or
not.  

If all constraints are of type 1, then T could be solved by interval
logic, narrowing the intervals for each variable as the constraints
are processed.  However, I'm not sure how to decide satisfiability
involving constraints of type 2.

Pointers to literature discussing efficient algorithms for this
problem, more general problems or similar problems are welcome.

--
         ) Andreas Zeller
    __o    Technische Universitaet Braunschweig, Abt. Softwaretechnologie
  _`\<,_   Gaussstrasse 17       Tel: +49 531/391-7580  zeller@acm.org
 ( )/ ( )  D-38092 Braunschweig  Fax: +49 531/391-8111  zeller@ips.cs.tu-bs.de
--^----^-- WWW: http://www.cs.tu-bs.de/softech/
