#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:                   |  
-------------------------------+--------------------------------------------
Changes (by mvngu):

  * reviewer:  => Minh Van Nguyen


Old description:

> This patch add to Sage the method Graph.induced_subgraph_search which
> looks for a given graph as an induced subgraph of "self".
>
> This is done through exhaustive search, using a very basic new graph
> class hand-made to efficiently stand such repetitive operations !
>
> I tried to document the code so that it could be somewhat easy to review,
> but feel free to ask any question about it ! :-)
>
> '''Apply:'''
>
>  1. #7529
>  1.
> [http://trac.sagemath.org/sage_trac/attachment/ticket/8922/trac_8922.patch
> trac_8922.patch]

New description:

 This patch add to Sage the method Graph.induced_subgraph_search which
 looks for a given graph as an induced subgraph of "self".

 This is done through exhaustive search, using a very basic new graph class
 hand-made to efficiently stand such repetitive operations !

 I tried to document the code so that it could be somewhat easy to review,
 but feel free to ask any question about it ! :-)

 '''Apply:'''

  1. #7529
  1.
 [http://trac.sagemath.org/sage_trac/attachment/ticket/8922/trac_8922.patch
 trac_8922.patch]
  1.
 
[http://trac.sagemath.org/sage_trac/attachment/ticket/8922/trac_8922-reviewer.patch
 trac_8922-reviewer.patch]

--

Comment:

 Changes in reviewer patch:

  * Move the method `adjacency_sequence()` to the class `CGraph`, as I
 think that method is useful for both dense and sparse graphs.
  * Clean-up coding style in accordance with PEP 008.
  * 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}`
  }}}
  I have used the latter formula in my reviewer patch. Please correct me if
 I'm wrong.
  * 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.
  * 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.

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

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8922#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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