MapReduce implementations of graph algorithms like PageRank and adsorption scale to millions of nodes on a cluster of around 50 machines, but if you want to process billions (or even tens of millions, depending on your algorithm) then you need a different framework. Google uses Pregel, about which they've said little except that it was inspired by the Bulk Synchronous Parallel model for parallel programming.
So the announcement of a BSP package for Hadoop in the Apache HAMA project could be an interesting one to watch. There's even a BSP hello world, although getting further may be hard work with the current level of documentation.
Tuesday, 6 April 2010
MapReduce algorithm design
Data-Intensive Text Processing with MapReduce is a new book by Jimmy Lin and Chris Dyer of the University of Maryland. It's due for publication later this year but a full draft is already available as a pdf. The book shows how you can implement a variety of useful algorithms on a MapReduce cluster, including graph algorithms such as breadth first search and PageRank, and parameter estimation for latent variable models, with a detailed explanation of how to do this for Hidden Markov Models, and even a sketch for Conditional Random Fields. Although the book is a practical manual, the algorithms are given in simple pseudo-code rather than Java classes intended for use on a Hadoop cluster. This has huge advantages for readability, and makes it much easier for the authors to draw out some generally applicable design patterns for MapReduce algorithms.
The order inversion pattern is a nice trick that lets a reducer see intermediate results before it processes the data that generated them. Lin and Dyer illustrate this with the example of computing relative frequencies for co-occurring word pairs e.g. what are the relative frequencies of words occurring within a small window of the word "dog"? The mapper counts word pairs in the corpus, so its output looks like
((dog, cat), 125)
((dog, foot), 246)
...
But it also keeps a running total of all the word pairs containing "dog", outputting this as
((dog,*), 5348)
Using a suitable partitioner, so that all (dog,...) pairs get sent to the same reducer, and choosing the "*" token so that it occurs before any word in the sort order, the reducer sees the total ((dog,*), 5348) first, followed by all the other counts, and can trivially store the total and then output relative frequencies. The benefit of the pattern is that it avoids an extra MapReduce iteration without creating any additional scalability bottleneck.
Other patterns explained in the book include the pairs and stripes approaches to produce large sparse matrix mapper output, in-mapper combining to limit the amount of mapper output written to disk (a common scalability bottleneck in MapReduce), and value-to-key conversion for relational joins of large datasets.
The order inversion pattern is a nice trick that lets a reducer see intermediate results before it processes the data that generated them. Lin and Dyer illustrate this with the example of computing relative frequencies for co-occurring word pairs e.g. what are the relative frequencies of words occurring within a small window of the word "dog"? The mapper counts word pairs in the corpus, so its output looks like
((dog, cat), 125)
((dog, foot), 246)
...
But it also keeps a running total of all the word pairs containing "dog", outputting this as
((dog,*), 5348)
Using a suitable partitioner, so that all (dog,...) pairs get sent to the same reducer, and choosing the "*" token so that it occurs before any word in the sort order, the reducer sees the total ((dog,*), 5348) first, followed by all the other counts, and can trivially store the total and then output relative frequencies. The benefit of the pattern is that it avoids an extra MapReduce iteration without creating any additional scalability bottleneck.
Other patterns explained in the book include the pairs and stripes approaches to produce large sparse matrix mapper output, in-mapper combining to limit the amount of mapper output written to disk (a common scalability bottleneck in MapReduce), and value-to-key conversion for relational joins of large datasets.
All in all, this book is a great complement to Tom White's Hadoop book. An extra plus is that the pseudo code can be translated with virtually no effort into dumbo code for Hadoop. I can see Data-Intensive Text Processing and dumbo becoming a standard way of teaching MapReduce quickly and excitingly in the classroom.
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