Hi Chao,
I implemented the 3-connectivity algorithm based on matroid intersection
last week. I did not implement Bixby-Cunningham and I did not essentially
change the implementation of matroid intersection, so there will be no need
to change any of your gsoc plans. But my new code is clearly in your path
this summer, so I thought I'd let you know. Perhaps the best way to reduce
any interference with the work you will be doing is to review my patch now,
so that it is part of sage by the time you start adding code.
While I was writing the code I noticed that the matroid intersection method
did not return an optimal dual solution, that is, a U so that max{ |X| : X
common independent set} = min { r_1(U) +r_2(E\U) }. I'm hoping you will
also add this functionality when you rewrite the cardinality matroid
intersection algorithm. I only partially did this now, to get minimal
matroid separations.
Best wishes,
Rudi
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