Messages in this thread | | | Date | Wed, 16 Nov 2011 11:28:42 +0100 | Subject | Re: [PATCH] perf_events: fix and improve x86 event scheduling | From | Stephane Eranian <> |
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On Mon, Nov 14, 2011 at 10:43 PM, Peter Zijlstra <peterz@infradead.org> wrote: > On Mon, 2011-11-14 at 18:39 +0100, Stephane Eranian wrote: >> On Mon, Nov 14, 2011 at 5:00 PM, Peter Zijlstra <peterz@infradead.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 > > Yeah, I found that, but that still reduces to O(c^2.5) which is over the > O(c^2) of Push relabel with dynamic trees. > > I haven't managed to wrap my head around this stuff well enough to even > start to have an idea if this constraint (bi-partite and unit > capacities) will have any considerable effect on the other algorithms. > > Also, we don't need an exhaustive max flow solution, any flow that's > high enough to fit the required capacity will do, this too could > possibly be used to lower the (average) complexity bound. > > I would really really like it to not average to O(n^3), that's just > silly expensive. > > Also, do you have any objections to me merging Roberts stuff (provided > it passes review etc.) while you poke at alternative solutions? We can > always replace the stuff again if we find anything that works better. > I don't have objections to Robert's patch. It will take a bit of time to come up with a good implementation of those max_flow algorithms. -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to majordomo@vger.kernel.org More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
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