Theoretically Grounded Pruning of Large Ground Sets for Constrained, Discrete Optimization
This addresses efficiency challenges in large-scale constrained optimization for applications like logistics or scheduling, though it is incremental as it builds on existing pruning methods.
The paper tackles the problem of billion-scale combinatorial optimization by developing a pruning algorithm to discard uninformative elements, demonstrating that QuickPrune prunes over 90% of the ground set and outperforms state-of-the-art heuristics.
Modern instances of combinatorial optimization problems often exhibit billion-scale ground sets, which have many uninformative or redundant elements. In this work, we develop light-weight pruning algorithms to quickly discard elements that are unlikely to be part of an optimal solution. Under mild assumptions on the instance, we prove theoretical guarantees on the fraction of the optimal value retained and the size of the resulting pruned ground set. Through extensive experiments on real-world datasets for various applications, we demonstrate that our algorithm, QuickPrune, efficiently prunes over 90% of the ground set and outperforms state-of-the-art classical and machine learning heuristics for pruning.