We acknowledge the reviewer's concern about extending our approach to distributed environments. However, we feel that this should not be a criticism of this paper, whose focus is on multicore systems which pose a unique set of challenges. Furthermore, we have shown that we can handle large graphs without stretching the limits of multicore systems.

Many machine learning problems can be reduced to the maximization of submodular functions. Although well understood in the serial setting, the parallel maximization of submodular functions remains an open area of research with recent results [1] only addressing monotone functions. The optimal algorithm for maximizing the more general class of non-monotone submodular functions was introduced by Buchbinder et al. [2] and follows a strongly serial double-greedy logic and program analysis. In this work, we propose two methods to parallelize the double-greedy algorithm. The first, coordination-free approach emphasizes speed at the cost of a weaker approximation guarantee. The second, concurrency control approach guarantees a tight 1/2-approximation, at the quantifiable cost of additional coordination and reduced parallelism. As a consequence we explore the tradeoff space between guaranteed performance and objective optimality. We implement and evaluate both algorithms on multi-core hardware and billion edge graphs, demonstrating both the scalability and tradeoffs of each approach.

Many machine learning problems can be reduced to the maximization of submodular functions. Although well understood in the serial setting, the parallel maximization of submodular functions remains an open area of research with recent results [1] only addressing monotone functions. The optimal algorithm for maximizing the more general class of non-monotone submodular functions was introduced by Buchbinder et al. [2] and follows a strongly serial double-greedy logic and program analysis. In this work, we propose two methods to parallelize the double-greedy algorithm. The first, coordination-free approach emphasizes speed at the cost of a weaker approximation guarantee. The second, concurrency control approach guarantees a tight 1/2-approximation, at the quantifiable cost of additional coordination and reduced parallelism. As a consequence we explore the tradeoff space between guaranteed performance and objective optimality. We implement and evaluate both algorithms on multi-core hardware and billion edge graphs, demonstrating both the scalability and tradeoffs of each approach.

Many machine learning problems can be reduced to the maximization of submodular functions.Although well understood in the serial setting, the parallel maximization of submodular functions remains an open area of research with recent results [1] only addressing monotone functions. The optimal algorithm for maximizing the more general class of non-monotone submodular functions was introduced by Buchbinder et al. [2] and follows a strongly serial double-greedy logic and program analysis. In this work, we propose two methods to parallelize the double-greedy algorithm. The first, coordination-free approach emphasizes speed at the cost of a weaker approximation guarantee. The second, concurrency control approach guarantees a tight 1/2-approximation, at the quantifiable cost of additional coordination and reduced parallelism. As a consequence we explore the tradeoff space between guaranteed performance and objective optimality. We implement and evaluate both algorithms on multi-core hardware and billion edge graphs, demonstrating both the scalability and tradeoffs of each approach.