> These are the times I get running the other solutions,
> 10 runs of 1000 points each.  Each run, every solution is
> fed the exact same point data.

Auuughhh!!

Sorry for another self-reply........ :-/

The benchmark script I attached to the earlier post did not,
in fact, pass the same point data to each solution per run.
(Maybe that'll teach me to make last minute changes without
verifying...)

The benchmark script at
http://tastyspleen.net/~billk/ruby/quiz/157-smallest-circle/benchmark/
now does correctly pass the same coordinate data to each script
per run.

 . . .

I had hoped by averaging multiple runs (10) - each run having
different point data - that the rankings would have been pretty
stable.

However, JUSTIN and LIONEL still tend to trade places on
different invocations:

             user     system      total        real
FRANK   24.421000   0.297000  24.718000 ( 24.734000)
JUSTIN   6.110000   0.000000   6.110000 (  6.109000)
LIONEL   6.078000   0.000000   6.078000 (  6.094000)
DOUG     3.750000   0.000000   3.750000 (  3.766000)
PHILIPP  1.609000   0.000000   1.609000 (  1.609000)
BILL     0.328000   0.000000   0.328000 (  0.328000)

             user     system      total        real
FRANK   24.656000   0.156000  24.812000 ( 24.828000)
LIONEL   6.047000   0.000000   6.047000 (  6.047000)
JUSTIN   4.375000   0.000000   4.375000 (  4.375000)
DOUG     3.281000   0.016000   3.297000 (  3.297000)
PHILIPP  1.500000   0.000000   1.500000 (  1.500000)
BILL     0.297000   0.000000   0.297000 (  0.297000)

             user     system      total        real
FRANK   24.594000   0.172000  24.766000 ( 24.781000)
LIONEL   6.109000   0.000000   6.109000 (  6.109000)
JUSTIN   5.922000   0.000000   5.922000 (  5.922000)
DOUG     4.031000   0.016000   4.047000 (  4.047000)
PHILIPP  1.344000   0.000000   1.344000 (  1.344000)
BILL     0.281000   0.000000   0.281000 (  0.282000)

             user     system      total        real
FRANK   24.203000   0.391000  24.594000 ( 24.672000)
LIONEL   6.109000   0.000000   6.109000 (  6.125000)
JUSTIN   5.500000   0.000000   5.500000 (  5.500000)
DOUG     4.188000   0.016000   4.204000 (  4.219000)
PHILIPP  1.500000   0.000000   1.500000 (  1.500000)
BILL     0.344000   0.000000   0.344000 (  0.344000)

             user     system      total        real
FRANK   24.546000   0.219000  24.765000 ( 24.765000)
JUSTIN   6.047000   0.015000   6.062000 (  6.062000)
LIONEL   5.828000   0.000000   5.828000 (  5.828000)
DOUG     3.641000   0.000000   3.641000 (  3.641000)
PHILIPP  1.688000   0.000000   1.688000 (  1.688000)
BILL     0.296000   0.000000   0.296000 (  0.296000)

(I have verified the rankings are stable if I hardwire
the random seed, though.)


Regards,

Bill