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From Christoph Schmitz <christoph.schm...@1und1.de>
Subject Re: How do I perform a scalable cartesian product
Date Thu, 15 Aug 2013 11:01:21 GMT
```Hi Steve,

if the only problem is that the size of your zipcode squared (more
accurately, n * (n-1) if you order the pairs of persons, assuming that
distance is symmetric) is too large, it might help to split the zipcode
into buckets by some hash function and partition the all-pairs
computations over buckets.

That is, if you have 10 buckets containing the users of a zipcode and
its neighboring zipcodes, first compute all pairs of persons within
bucket 1, then all pairs of persons in bucket 1 and 2, then 1-3, 1-4
etc. up to 10-10. Obviously, you don't need to do 4-1 if you've already
done 1-4 (symmetry, see above), so you'll end up doing n * (n+1) pairs
of buckets (55 in this case).

Basically, this means creating artificial, smaller zipcodes.

Apart from that, I'd like to point out that there's been a lot of
research on nearest-neighbor search; perhaps some state-of-the-art
algorithm will be applicable to your problem.

http://en.wikipedia.org/wiki/Nearest_neighbor_search

Hope this helps,

Christoph

On 14.08.2013 19:06, Steve Lewis wrote:
>    I have the problem of performing a operation of a data set on itself.
>
>     Assume, for example, that I have a list of people and their
> addresses and for each person I want the ten closest members of the set.
> (this is not the problem but illustrated critical aspects). I know that
> the ten closest people will be in the same zipcode or a neighboring zip
> code. This means unless the database is very large I can have the mapper
> send every person out with keys representing  their zipcode and also
> keys representing the neighboring zip codes. In the reducer I can keep
> all people in memory and compute distances between them (assume the
> distance computation is slightly expensive).
>     The problem is that this approach will not scale - eventually the
> number of people assigned to a zip code will exceed memory. In the
> current problem the number of "people" is about 100 million and doubling
> every 6 months. The size of a "zipcode" requires keeping about 100,000
> items in memory - doable today but marginal in terms of future growth.
>     Are there other ways to solve the problem. I considered keeping a
> random subset, finding the closest in that subset and then repeating
> with different random subsets. The solution of midifying the splitter to
> generate all pairs
> https://github.com/adamjshook/mapreducepatterns/blob/master/MRDP/src/main/java/mrdp/ch5/CartesianProduct.java
will
> not work for a dataset with 100 million items
>     Any bright ideas?
>
>
>
>

--
Christoph Schmitz
Software-Architekt
Targeting Core Product

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