[R] Suggestion for big files [was: Re: A comment about R:]

r.ghezzo@staff.mcgill.ca r.ghezzo at staff.mcgill.ca
Mon Jan 9 14:44:19 CET 2006

I found Reservoir-Sampling algorithms of time complexity O(n(1+log(N/n))) by
Kim-Hung Li , ACM Transactions on Mathematical Software Vol 20 No 4 Dec 94
He mentions algorithm Z and K and proposed 2 improved versions alg L and M.
Algorith L is really easy to implement but relatively slow, M doesn't look very
difficult and is the fastest.
Heberto Ghezzo
McGill University
Montreal - Canada

Quoting François Pinard <pinard at iro.umontreal.ca>:

> [Martin Maechler]
> >    FrPi> Suppose the file (or tape) holds N records (N is not known
> >    FrPi> in advance), from which we want a sample of M records at
> >    FrPi> most. [...] If the algorithm is carefully designed, when
> >    FrPi> the last (N'th) record of the file will have been processed
> >    FrPi> this way, we may then have M records randomly selected from
> >    FrPi> N records, in such a a way that each of the N records had an
> >    FrPi> equal probability to end up in the selection of M records.  I
> >    FrPi> may seek out for details if needed.
> >[...] I'm also intrigued about the details of the algorithm you
> >outline above.
> I went into my old SPSS books and related references to find it for you,
> to no avail (yet I confess I did not try very hard).  I vaguely remember
> it was related to Spearman's correlation computation: I did find notes
> about the "severe memory limitation" of this computation, but nothing
> about the implemented workaround.  I did find other sampling devices,
> but not the very one I remember having read about, many years ago.
> On the other hand, Googling tells that this topic has been much studied,
> and that Vitter's algorithm Z seems to be popular nowadays (even if not
> the simplest) because it is more efficient than others.  Google found
> a copy of the paper:
>    http://www.cs.duke.edu/~jsv/Papers/Vit85.Reservoir.pdf
> Here is an implementation for Postgres:
>    http://svr5.postgresql.org/pgsql-patches/2004-05/msg00319.php
> yet I do not find it very readable -- but this is only an opinion: I'm
> rather demanding in the area of legibility, while many or most people
> are more courageous than me! :-).
> --
> François Pinard   http://pinard.progiciels-bpi.ca
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