What type of problems can mapreduce solve?

In Map-Reduce for Machine Learning on Multicore Chu et al describe “algorithms that fit the Statistical Query model can be written in a certain “summation form,” which allows them to be easily parallelized on multicore computers.” They specifically implement 10 algorithms including e.g. weighted linear regression, k-Means, Naive Bayes, and SVM, using a map-reduce framework.

The Apache Mahout project has released a recent Hadoop (Java) implementation of some methods based on the ideas from this paper.

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