Theoretically Grounded Pruning of Large Ground Sets for Constrained, Discrete Optimization

TL;DR

This paper introduces QuickPrune, a theoretically grounded and efficient pruning algorithm that reduces large ground sets in combinatorial optimization problems by over 90%, improving solution efficiency and quality.

Contribution

The paper presents a novel, light-weight pruning algorithm with theoretical guarantees, outperforming existing heuristics in large-scale combinatorial optimization.

Findings

Prunes over 90% of ground set elements.

Retains a significant fraction of optimal value.

Outperforms classical and machine learning heuristics.

Abstract

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.