[tahoe-dev] "servers of happiness" Re: MapReduce over Tahoe-LAFS slides from HadoopWorld

[Kevan Carstensen]

On 10/15/09 12:02 AM David-Sarah Hopwood <david-sarah at jacaranda.org>
wrote:
> Or do you mean:
>     2. Any k of the peers to which shares went are sufficient to
>        reconstruct the file.

In most cases, this is correct. It breaks down if there are two peers in
the grid that store the same share, though -- in this case, we cannot
guarantee that formulation of 2.

More formally:

  1. There exists a set of peers with at least size h such that an
     injection can be created between peers in that set and shares
  2. Any k of the peers in that set is sufficient to reconstruct the
     file.

Though, worded like that, the second condition is redundant -- if my
proof isn't wrong, I've shown that the first condition implies the
second. So maybe it is just

  1. There exists a set of peers with cardinality at least h such that
     an injection can be crafted between peers in the set and shares.

If it is pared down to that, though, I think I prefer Zooko's way of
thinking about health -- it goes much farther in actually explaining
what a health value of h actually means.

Thanks for the question -- it is useful to clarify these things,
especially after a lengthy discussion such as in #778.
-- 
Kevan Carstensen | <kevan at isnotajoke.com>