Re: Growth rate

Karl J. Runge (runge@redhook.llnl.gov)
Thu, 24 Apr 97 15:57:56 PDT


On Thu, 24 Apr 97, "Colin L. Hildinger" <colin@ionet.net> wrote:
> On Thu, 24 Apr 1997 10:30:21 -0500 (EST), Michael J Gebis wrote:
>
> >For the first half of the curve, the growth looks exponential. I fear
> >that we have passed this point, and are nearing the linear part of the
> >curve. For example, the "doubles every week" rule of thumb hasn't held for
> >the past few days.
>
> I'm guessing that it has to do with the weekend ending and the bad data
> point on Monday. If you look back historically, there have always been
> dropoffs after the weekends, so the current data doesn't supprise me.
> The test will be if we break ~100000000000000 keys this Friday or
> Saturday, then we'll know growth is continuing as scheduled.

The best we can hope for is for a good number of places like uiuc to keep
coming on board!

> >> >A calculation I have worked out in a notebook but not coded up to get the
> >> >numbers for is computing (ave_time_uncoordinated/ave_time_coordinated)
> >> >not assuming a constant key rate, but instead a rapidly growing one.
> >> >We've had exponential growth with doubling time of 7-8 days for well
> >> >over a month now, I hope it lasts a good while longer.
> >>
> >> This is a feasible calc. but, from looking at the graphs I'd say that we
> >> may have linear growth instead of exponential growth. Though I could be
> >> incorrect...:)

FWIW, I've done the calculations of the average time to find the key
for two cooperating and two non-cooperating keyservers. They serve out
keys at equal rates, but the rate increases with time.

== Fit to exponential growth starting 3/14/97

ave time for 2 cooperating keyservers 66.8 days.
ave time for 2 NONcooperating servers 68.7 days.

I'm pretty sure this result is correct, kind of amazing cooperation
only makes a difference of a couple days. This is because so many keys
are being checked near the end. I guess our 10% daily growth rate probably
can't be sustained to the end of the search, but maybe we'll be lucky
and get a good chunk of it.

== Fit to LINEAR growth over last 12 days

ave time for 2 cooperating keyservers 109 days. (from 3/14/97)
ave time for 2 NONcooperating servers 121 days. (from 3/14/97)

I guess a linear growth rate at the current rate is more practical.
Still, only a 12 days (on average) gain from cooperation.

So now I know when it doesn't pay to cooperate. My two kids have been
trying to teach me this by example for years!

Karl

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Karl J. Runge -- Linux: it's the Real thing -- runge@crl.com
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