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<html><head><meta content="text/html; charset=ISO-8859-1" http-equiv="Content-Type"><title>Constraint Propagation in Python</title><meta name="generator" content="LOGILAB adaptation of DocBook XSL Stylesheets V1.29"><meta name="language" content="en"><meta name="organization" content="Logilab S.A."></head><body bgcolor="#FFFFFF" text="#000000"><table border="0" width="100%" cellspacing="2" cellpadding="0"><tr><td width="20%"><img src="file:/home/logilab/public/logos/logilab.gif" width="150"></td><td width="80%"><h3 class="template"><center>Constraint Propagation in Python</center></h3><hr noshade="yes" size="5" width="100%"></td></tr></table><table width="100%" cellspacing="0" cellpadding="8"><tr><td width="5%" bgcolor="#FFAA1B" valign="top" align="left"></td><td width="95%" valign="top" align="left"><div id="constraint-propagation-manual" class="article"><div class="article"><p></p><h1 class="title0"><center>Constraint Propagation in Python</center></h1><h2 class="subtitle0"><center><i></i></center></h2><p></p><table border="0" width="100%"><tr><td width="50%"><p align="left"><b>Alexandre Fayolle</b></p></td><td width="50%"></td></tr></table><hr width="100%"><p></p><h3 class="titlepage-title">Copyright 2002 by Logilab</h3>This manual presents how to use the constraint package to solve
constraint propagation problems in Python. It also presents the
the extension mechanisms available in the package</div><div class="sect1"><a name="using"></a><div class="sect1"><p></p><h1 class="title2"><a name="using"></a>1. Using the constraint package<br><hr width="100%"></h1></div><div class="sect2"><a name="id2709498"></a><div class="sect2"><h2 class="title3"><a name="id2709498"></a>1.1. Sample problem</h2></div><p>Let's take a real-life problem to get started. You're organising a
an international Python Programming event, and you have to schedule
conferences. There are 10 different conferences, you have 3 conference
rooms available during 2 days. Each conference is 4 hours long, so you
can organize at most 2 conferences per day in a given room.</p><p>Conferences 3, 4, 5 and 6 have to take place in room C, because
it's the only one with Internet access.</p><p>Some of the speakers are not available on both days, so
conferences 1, 5 and 10 have to take place on day 1, and conferences 2,
3 4 and 9 on day 2.</p><p>You have made a quick poll over the python mailing list, and it
turns out that people attending some of the conferences are likely to be
attending some other conferences too, so you want to make sure that such
conferences are not scheduled at the same time. A careful statistical
study has found 4 groups of potential attendees. The first group want to
attend conferences 1, 2, 3 and 10, the second conferences 2, 6, 8 and 9
the third group conferences 3, 5, 6 and 7, and the last group
conferences 1, 3, 7 and 8.</p><p>You've tried to put this on a whiteboard, but this quickly proved
to be tedious, so you thought about using the constraint solving
package.</p></div><div class="sect2"><a name="id2709551"></a><div class="sect2"><h2 class="title3"><a name="id2709551"></a>1.2. Variables, Domains and Constraints</h2></div><p>The first thing to find out in order to use the constraint package
is what the variables are, what their domains are and what the
constraints between variables are.</p><p>If we look at our problem, the variables are the conferences' room
and time slot, and for each conference, the domain is the cross product
of the set of available rooms with the set of available time slots. We
could say that the conferences which require Internet access have a
different domain, because they need to be in room C. This is perfectly
valid. However, we will model this as a constraint.</p><p>Variables are manipulated as names, stored in character
strings. Domains are instances of the fd.FiniteDomain class, which is
instantiated with a list of values. Domains are manipulated through a
dictionnary mapping a variable to its domain. Do not use the same domain
instance for several variables, because in the current implementation,
this is guaranteed to break. The code looks like this:
<pre class="programlisting">
<font color="#008000"># import Repository class and fd module, </font>
<font color="#C00000">from</font> logilab.constraint <font color="#C00000">import</font> *
variables = (<font color="#004080">'c01'</font>,<font color="#004080">'c02'</font>,<font color="#004080">'c03'</font>,<font color="#004080">'c04'</font>,<font color="#004080">'c05'</font>,<font color="#004080">'c06'</font>,<font color="#004080">'c07'</font>,<font color="#004080">'c08'</font>,<font color="#004080">'c09'</font>,<font color="#004080">'c10'</font>)
values = [(room,slot)
<font color="#C00000">for</font> room <font color="#C00000">in</font> (<font color="#004080">'room A'</font>,<font color="#004080">'room B'</font>,<font color="#004080">'room C'</font>)
<font color="#C00000">for</font> slot <font color="#C00000">in</font> (<font color="#004080">'day 1 AM'</font>,<font color="#004080">'day 1 PM'</font>,<font color="#004080">'day 2 AM'</font>,<font color="#004080">'day 2 PM'</font>)]
domains = {}
<font color="#C00000">for</font> v <font color="#C00000">in</font> variables:
domains[v]=fd.FiniteDomain(values)
</pre>
</p><p>Constraints, like domains are objects. So far the only class that
can be used is fd.Expression and fd.BinaryExpression. We use the
fd.make_expression factory function to build an instance of the right
class, depending on the number of variables that is passed. This
function takes a list of affected variables and a python expression that
evaluates to true if the constraint is satisfied. </p><p>We have several constraints on our variables. First some
conferences need to take place in room C:
<pre class="programlisting">
constraints = []
<font color="#C00000">for</font> conf <font color="#C00000">in</font> (<font color="#004080">'c03'</font>,<font color="#004080">'c04'</font>,<font color="#004080">'c05'</font>,<font color="#004080">'c06'</font>):
constraints.append(fd.make_expression((conf,),
"%s[0] == 'room C'"%conf))
</pre>
</p><p>Availability of the speakers impose some more constraints:
<pre class="programlisting">
<font color="#C00000">for</font> conf <font color="#C00000">in</font> (<font color="#004080">'c01'</font>,<font color="#004080">'c05'</font>,<font color="#004080">'c10'</font>):
constraints.append(fd.make_expression((conf,),
"%s[1].startswith(<font color="#004080">'day 1'</font>)"%conf))
<font color="#C00000">for</font> conf <font color="#C00000">in</font> (<font color="#004080">'c02'</font>,<font color="#004080">'c03'</font>,<font color="#004080">'c04'</font>,<font color="#004080">'c09'</font>):
constraints.append(fd.make_expression((conf,),
"%s[1].startswith(<font color="#004080">'day 2'</font>)"%conf))
</pre>
</p><p>Then we want to say that some of the conferences should not be
scheduled at the same time:
<pre class="programlisting">
groups = ((<font color="#004080">'c01'</font>,<font color="#004080">'c02'</font>,<font color="#004080">'c03'</font>,<font color="#004080">'c10'</font>),
(<font color="#004080">'c02'</font>,<font color="#004080">'c06'</font>,<font color="#004080">'c08'</font>,<font color="#004080">'c09'</font>),
(<font color="#004080">'c03'</font>,<font color="#004080">'c05'</font>,<font color="#004080">'c06'</font>,<font color="#004080">'c07'</font>),
(<font color="#004080">'c01'</font>,<font color="#004080">'c03'</font>,<font color="#004080">'c07'</font>,<font color="#004080">'c08'</font>))
<font color="#C00000">for</font> g <font color="#C00000">in</font> groups:
<font color="#C00000">for</font> conf1 <font color="#C00000">in</font> g:
<font color="#C00000">for</font> conf2 <font color="#C00000">in</font> g:
<font color="#C00000">if</font> conf2 > conf1:
constraints.append(fd.make_expression((conf1,conf2),
<font color="#004080">'%s[1] != %s[1]'</font>%\
(conf1,conf2)))
</pre>
</p><p>Finally, no two conferences can be scheduled in the same room at
the same time:
<pre class="programlisting">
<font color="#C00000">for</font> conf1 <font color="#C00000">in</font> variables:
<font color="#C00000">for</font> conf2 <font color="#C00000">in</font> variables:
<font color="#C00000">if</font> conf2 > conf1:
constraints.append(fd.make_expression((conf1,conf2),
<font color="#004080">'%s != %s'</font>%(conf1,conf2)))
</pre>
</p></div><div class="sect2"><a name="id2706665"></a><div class="sect2"><h2 class="title3"><a name="id2706665"></a>1.3. The Repository class</h2></div><p>Repository objects are used to hold the variables, domains and
constraints describing the problem. A Solver object can solve the
problem described by a Repository.</p><p>Here's the final touch:
<pre class="programlisting">
r = Repository(variables,domains,constraints)
solutions = Solver().solve(r)
<font color="#C00000">print</font> solutions
</pre>
</p></div><p>The code is available in the file conferences.py in the examples
directory of the distribution. It finds 64 possible schedules in a
couple of seconds on my machine.</p><div class="sect2"><a name="id2706710"></a><div class="sect2"><h2 class="title3"><a name="id2706710"></a>1.4. Performance considerations</h2></div><p>There is still a lot of things to be worked on with this
package. Here are a few tips that can help you to use it in its
current state:
<div class="itemizedlist"><ul><li><a name="id2706724"></a><p class="in-li"><a name="id2706724"></a>Try to avoid constraints with a lot of variables. It
is better to have several binary constraints than one big N-ary
constraint with several 'and' conditions</p></li><li><a name="id2706733"></a><p class="in-li"><a name="id2706733"></a>If you cannot avoid constraint with lots of
variable, put the constraints with less variables first in the list,
because they will get evaluated before, will take less time to
process, and will hopefully reduce the domains of the variables
playing a role in your big constraints</p></li></ul></div>
</p></div></div><div class="sect1"><a name="extending"></a><div class="sect1"><p></p><h1 class="title2"><a name="extending"></a>2. Extending the constraint package<br><hr width="100%"></h1></div><p>WRITE ME!</p></div></div></td></tr></table></body></html>
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