I thought matching was a dual of max flow, so weighted matching was a dual
of min cost max flow (relabling edges with infinity minus cost).

The simplest algorithm to implement would be Ford-Fulkerson with
Floyd-Warshall to find augmenting paths.  The most efficient would be
Dinic's, I think?




On Tue, Mar 18, 2014 at 11:25 AM, Laurens Van Houtven <_...@lvh.cc> wrote:

> Hi,
>
>
> On Tuesday, March 18, 2014 3:02:01 PM UTC+1, Paul deGrandis wrote:
>
>> I've written general versions of Blossom and Blossom V in the past, and
>> every so often a similar question comes up on this mailing list.
>>
>
> I'm guessing that wasn't in clojure? :-(
>
> Do you happen to know what happens when you throw Blossom V at a graph
> that doesn't have a perfect matching? E.g. for my use case, hotel room
> pairing, there's a 1/2 chance the graph ends up having an odd number of
> nodes... IIUC it won't terminate, but you can detect that it won't, so then
> you can just give the best-effort solution anyway?
>
>
>> I'd personally love to see both algorithms contributed to Loom if OP is
>> up for the task.
>>
>
> I'm afraid I've got a convex optimization problem in terms of financial
> aid grant sizes to solve first before I can start writing that code :-)
>
> cheers
> lvh
>
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