Re: [PATCH] perf_events: fix and improve x86 event scheduling

[Peter Zijlstra <peterz@infradead.org>]

On Mon, 2011-11-14 at 15:26 +0100, Stephane Eranian wrote:
> There is an edge from the source to all the events.
> There is an edge from all the counters to the sync.
> There is an edge between an event and a counter, if
> it can count the event.
> 
> The capacity of any edge is 1. 

Ah indeed.

So that gives: 

 E = e+e*c+c ~= O(c^2); since e<=c
 V = 2+e+c   ~= O(c)

Then going by:

http://en.wikipedia.org/wiki/Maximum_flow_problem

we have to stay away from Edmonds-Karp.

Ford-Fulkerson would end up being O(E * c) = O(c^3), since max |f| is c.
Which is pretty much identical to all these O(V^2 E) = O(c^3) as well.

Dinitz blocking flow with dynamic trees looks more interesting at O(c^2
log(c)). Push relabel with dynamic trees looks to be best at O(c^2),
since V^2/E ends up being c^2/c^2 = 1.

Creating the graph itself will be O(c^2) as well, due to E.