[RC5] Long-term projects: exponential and logarithmic growth

Daniel Quintiliani danq at ptd.net
Sat Sep 4 10:10:48 EDT 2004


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Remember a month ago I suggested that with long-term distributed computing projects,
logarithmic growth is a better estimate than exponential growth because people leave the
project or die as processing power grows?

I just looked at the OGRp1 graphs <http://www1.distributed.net/~pstadt/ogr/> and noticed 
that the processing power growth did not catch up to the amount of people who left the project.

However, when I plotted (this time by month, not half-month, because I didn't feel like it) estimates
of the rate in Tnodes/sec from every month of the OGRp1 project, the R^2 value of the logarithmic
growth was 0.0631 and the R^2 value of the exponential growth was 0.0453. Both values are low,
since it wasn't even close to logarithmic growth due to more people leaving than processor power 
growing, but logarithmic growth was still a better estimate if you added up all of the estimated average 
nodes/month (31,837,855,980,401,200,000 total for logarithmic, 24,832,936,897,178,500,000 total for
exponential) and the real average nodes/month (32,399,136,000,000,000,000 total). I don't know the actual
total OGRp1 stubs, does anyone know them or if I was close?

I also looked at the OGRp2 graphs and plotted by half-month. Even with only three month's data, logarithmic
growth still produced a better R^2 value (0.9246) than exponential growth (0.5271).

As for RC5 and those predictions, I updated the sheet at mid-August (452y 6mo R^2=0.8621) and September 1st (454y
6mo R^2=0.8645). So it basically comes down to the fact that RC5 will take at least 450 years to complete, not 17.

So, basically, logarithmic growth provides a better, but nowhere near perfect, estimate, and RC5 will take AT LEAST
450 years to complete (from Dec 2002).

- --

- -Dan
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