Re: [Haskell-cafe] What class for splittable data / balanced-fold?

I've got a Partitionable class that I've been using for this purpose: https://github.com/mikeizbicki/ConstraintKinds/blob/master/src/Control/Const... The function called "parallel" in the HLearn library will automatically parallelize any homomorphism from a Partionable to a Monoid. I specifically use that to parallelize machine learning algorithms. I have two thoughts for better abstractions: 1) This Partitionable class is essentially a comonoid. By reversing the arrows of mappend, we get: comappend :: a -> (a,a) By itself, this works well if the number of processors you have is a power of two, but it needs some more fanciness to get things balanced properly for other numbers of processors. I bet there's another algebraic structure that would capture these other cases, but I'm not sure what it is. 2) I'm working with parallelizing tree structures right now (kd-trees, cover trees, oct-trees, etc.). The real problem is not splitting the number of data points equally (this is easy), but splitting the amount of work equally. Some points take longer to process than others, and this cannot be determined in advance. Therefore, an equal split of the data points can result in one processor getting 25% of the work load, and the second processor getting 75%. Some sort of lazy Partitionable class that was aware of processor loads and didn't split data points until they were needed would be ideal for this scenario. On Sat, Sep 28, 2013 at 6:46 PM, adam vogt wrote:

On Sat, Sep 28, 2013 at 1:09 PM, Ryan Newton wrote:

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Hi all,

We all know and love Data.Foldable and are familiar with left folds and right folds. But what you want in a parallel program is a balanced fold over a tree. Fortunately, many of our datatypes (Sets, Maps) actually ARE balanced trees. Hmm, but how do we expose that?

Hi Ryan,

At least for Data.Map, the Foldable instance seems to have a reasonably balanced fold called fold (or foldMap):

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fold t = go t where go (Bin _ _ v l r) = go l `mappend` (v `mappend` go r)

This doesn't seem to be guaranteed though. For example ghc's derived instance writes the foldr only, so fold would be right-associated for a:

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data T a = B (T a) (T a) | L a deriving (Foldable)

Regards, Adam _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe