#8922: induced subgraph search
-------------------------------+--------------------------------------------
   Reporter:  ncohen           |       Owner:  jason, ncohen, rlm
       Type:  enhancement      |      Status:  needs_review      
   Priority:  critical         |   Milestone:  sage-4.4.4        
  Component:  graph theory     |    Keywords:                    
     Author:  Nathann Cohen    |    Upstream:  N/A               
   Reviewer:  Minh Van Nguyen  |      Merged:                    
Work_issues:                   |  
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Comment(by ncohen):

 Hello !!

 First, I want to thank you for the amount of time your must have spent on
 this :-)

 >  * Move the method `adjacency_sequence()` to the class `CGraph`, as I
 think that method is useful for both dense and sparse graphs.

 It can be, though systematically testing adjacencies (and most importantly
 -- non-adjacencies) in sparse graph can be a problem... Perhaps we will
 have to split this function in two copies, one for each class, one day or
 another. I have been talking with Alexandre Blondin Masse who could need
 such a feature for Sparse graphs :-)

 >  * In describing the algorithm used in `subgraph_search()` of the module
 `generic_graph_pyx.pyx`, you have the formula:
 >  {{{
 > `\binom k!{|V(G)|}{k}`
 >  }}}
 >  That won't typeset in LaTeX as you expected. Do you mean this?
 >  {{{
 > `k! \binom{|V(G)|}{k}`
 >  }}}

 Indeed

 >  I have used the latter formula in my reviewer patch. Please correct me
 if I'm wrong.

 You almost never are :-)

 >  * Unit tests for the `cdef` functions `vectors_equal()` and
 `vectors_inferior()`, and the method `adjacency_sequence()`. These
 functions/methods are defined using `cdef` and the doctest coverage script
 don't pick them up in its analysis. However, I still think it's important
 to provide unit tests for such functions/methods.

 Well, if there is anything wrong in these functions your tests will show
 it, though given their length I wouldn't have thought necessary to add
 such tests.... Are you doubting Cython itself ? :-)

 >  * Amalgamate the methods `induced_subgraph_search()` and
 `subgraph_search()`. Their definitions are almost identical, except for
 the keyword `induced`. The combined method is defined to take the boolean
 keyword `induced` and pass it on to the relevant method.

 I was thinking of someone working on induced subgraphs, and not seeing any
 occurence of this word among the functions.... But he will get interested
 in subgraph search sooner or later ;-)

 > Another pair of eyes is needed to look over my reviewer patch.

 I already spent some time over it, and agreed with what I saw....
 Considering its length, I may do this once or twice again before setting
 it to "positive review". and... Thank you again :-)

 Nathann

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8922#comment:13>
Sage <http://www.sagemath.org>
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