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

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Date:	Mon, 14 Nov 2011 18:39:29 +0100
From:	Stephane Eranian <eranian@...gle.com>
To:	Peter Zijlstra <peterz@...radead.org>
Cc:	Robert Richter <robert.richter@....com>,
	"linux-kernel@...r.kernel.org" <linux-kernel@...r.kernel.org>,
	"mingo@...e.hu" <mingo@...e.hu>,
	"ming.m.lin@...el.com" <ming.m.lin@...el.com>,
	"ak@...ux.intel.com" <ak@...ux.intel.com>
Subject: Re: [PATCH] perf_events: fix and improve x86 event scheduling

On Mon, Nov 14, 2011 at 5:00 PM, Peter Zijlstra <peterz@...radead.org> wrote:
> 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.
>
I think we are in the special case of a bi-partite graph with unit capacities,
thus the complexity can be reduced even more.

See Special Cases in http://en.wikipedia.org/wiki/Dinic%27s_algorithm
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