Ravi Kumar
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Abstract
Greedy algorithms are practitioners’ best friends—they are intuitive, are simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power.
Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. Armed with this primitive, we then adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraint problems. Our method yields efficient algorithms that run in a logarithmic number of rounds while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system constraints.
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Index Terms
- Fast Greedy Algorithms in MapReduce and Streaming
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