[mnet-devel] about choice of redundancy factor

[Zooko]

Thanks to Kyle's graphs [1] I now have some justification about why 
I intuitively favor a redundancy factor greater than 2.  That justification is 
that what we are interested in is the high-reliability part of the graph, where 
the curve goes to y >= 0.98 or so.

(y represents the probability of recovering a file, x represents the probability 
of recovering an arbitrary share.)

For y to get that high, x has to be > K/M, where K is the required-shares and 
M is the total-shares.  (M/K, or "R" is the "redundancy".)

That, I already knew.  But the graphs reminded me of the additional fact that 
the threshold that x has to reach is somewhat *higher* than K/M.  For example, 
in the 12-of-24 graph [2] shows that x has to reach about 0.75 (where K/M is 
0.5) for y to reach about 0.98.  In the 6-of-24 graph [3] it appears that 
x needs to reach about 0.5 (where K/M is 0.25) for y to reach about 0.98.

So somehow this strengthens my intuition that making K/M be around 1/4 is 
substantially more robust than making it be around 1/2.

--Z

[1] http://www.toehold.com/~kyle/mn/
[2] http://www.toehold.com/~kyle/mn/get12of24.png
[3] http://www.toehold.com/~kyle/mn/get6of24.png


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