Accelerated Best-First Search With Upper-Bound Computation for Submodular Function Maximization

Submodular maximization continues to be an attractive subject of study thanks to its applicability to many real-world problems. Although greedy-based methods are guaranteed to find (1− 1/e)-approximate solutions for monotone submodular maximization, many applications require solutions with better approximation guarantees; moreover, it is desirable to be able to control the trade-off between the computation time and approximation guarantee. Given this background, the bestfirst search (BFS) has been recently studied as a promising approach. However, existing BFS-based methods for submodular maximization sometimes suffer excessive computation cost since their heuristic functions are not well designed. In this paper, we propose an accelerated BFS for monotone submodular maximization with a knapsack constraint. The acceleration is attained by introducing a new termination condition and developing a novel method for computing an upper-bound of the optimal value for submodular maximization, which enables us to use a better heuristic function. Experiments show that our accelerated BFS is far more efficient in terms of both time and space complexities than existing methods.