Max-Cover in Map-Reduce

The NP-hard Max-k-cover problem requires selecting k sets from a collection so as to maximize the size of the union. This classic problem occurs commonly in many settings in web search and advertising. For moderately-sized instances, a greedy algorithm gives an approximation of (1-1/e). However, the greedy algorithm requires updating scores of arbitrary elements after each step, and hence becomes intractable for large datasets. We give the first max cover algorithm designed for today's large-scale commodity clusters. Our algorithm has provably almost the same approximation as greedy, but runs much faster. Furthermore, it can be easily expressed in the MapReduce programming paradigm, and requires only polylogarithmically many passes over the data. Our experiments on five large problem instances show that our algorithm is practical and can achieve good speedups compared to the sequential greedy algorithm.

• Algorithms and Theory