#12716: MILP formulation and test functions for vertex separation
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       Reporter:  dcoudert                                          |         
Owner:  jason, ncohen, rlm
           Type:  enhancement                                       |        
Status:  needs_work        
       Priority:  major                                             |     
Milestone:  sage-5.0          
      Component:  graph theory                                      |    
Resolution:                    
       Keywords:  graph, decomposition, linear ordering, pathwidth  |   Work 
issues:                    
Report Upstream:  N/A                                               |     
Reviewers:  Nathann Cohen     
        Authors:  David Coudert                                     |     
Merged in:                    
   Dependencies:                                                    |      
Stopgaps:                    
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Changes (by ncohen):

  * status:  needs_review => needs_work


Comment:

 Helloooooooooo David !!!

 Here is a small patch to apply on top of yours.. Here is what it does :

     * One or two typoes
     * Simplifies the definition of the LP variables... Could you give it a
 look, just to check I got nothing wrong ? `:-)`
     * Replaces some lists operation by set operations. Well, it looked
 like all you wanted to do was more a set thing than a list thing.
     * Replaces some integer = True by binary = True. The solvers (well,
 except Coin as usual) have specific types for binary variables, so if we
 know that they are binary we may as well say it.
     * I also moved several lines of code outside of the try/catch, as list
 operations usually do not throw MIPSolverExceptions

 I also have several questions :
     * Could you say in the doc which variables are relaxed when
 integrality=False, and if it has any specific meaning ? Or is it just a
 lower bound that you use because it is faster ?
     * Is the integrality variable really intended to be False **by
 default** ? `O_o;;;`
     * About constraints 5, 6, and 7 : why aren't they all set by "sum of
 all y[v][t] for all v is equal to t" ? Or rather to t+1 ? I do not get why
 you do not say so immediately to the solver `O_o`
     * To me ``u[v][t] >= x[v][t]-y[v][t]`` is rather ``x[v][t] == u[v][t]
 + y[v][t]``, which is the same constraint but in a way I find easier to
 read.. That's one of the remarks I added to the definition of the
 variables, though `:-)`

 Well, I think that's all I had to say !

 Nathann

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12716#comment:4>
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