Ankur Nath, Alan Kuhnle

Hierarchical DeepPruner: A Novel Framework for Search Space Reduction

Introduction

Hierarchical deeppruner: a novel framework for search space reduction. Hierarchical DeepPruner: a novel framework for efficient search space reduction in NP-hard combinatorial optimization on graphs, achieving significant speedups and quality.

Abstract

Combinatorial optimization (CO) problems on graphs arise in various applications across diverse domains. Many of these problems are NP-hard, and heuristics have been developed to provide near-optimal solutions. In the big data era, the high dimensionality of these problems poses significant challenges for existing heuristic methods, which struggle to scale efficiently. In this paper, we propose Hierarchical DeepPruner, an adaptive framework that employs a two-stage approach to efficiently prune the search space of CO problems on graphs. Compared to state-of-the-art pruning heuristics, our algorithm offers two key advantages: 1) it does not require extensive feature engineering or domain-specific knowledge, and 2) it outperforms all previous methods while consistently pruning over 95% of the ground set, resulting in up to several of tenfold speedups—typically with minimal impact on solution quality. Additionally, our algorithm can successfully reduce the search space of instances even if they lie outside the training distribution, resulting in small optimality gaps across multiple budgets

Review

This paper introduces Hierarchical DeepPruner, a novel framework designed to tackle the significant computational challenges posed by NP-hard Combinatorial Optimization (CO) problems on graphs, particularly in high-dimensional big data contexts. The abstract effectively highlights the pressing need for scalable solutions, as existing heuristic methods struggle to maintain efficiency. The proposed two-stage adaptive approach aims to substantially prune the search space, offering a promising avenue for improving the tractability of these complex problems. Given the widespread applicability of CO problems across diverse domains, a framework that can enhance the scalability and efficiency of their resolution is highly relevant and timely. The core contributions of Hierarchical DeepPruner, as outlined, are particularly compelling. The framework claims to overcome two major limitations of prior pruning heuristics: an independence from extensive feature engineering and domain-specific knowledge, which significantly broadens its applicability and reduces development overhead. Furthermore, the paper asserts that Hierarchical DeepPruner not only outperforms state-of-the-art methods but also achieves remarkable search space reduction, consistently pruning over 95% of the ground set. This level of reduction is purported to lead to substantial speedups, up to several tens of times, typically without compromising solution quality, suggesting a significant leap in efficiency. A notable strength highlighted in the abstract is the algorithm's robustness, demonstrated by its ability to reduce search space and maintain small optimality gaps even when instances lie outside the training distribution, across multiple budgets. This indicates a strong generalization capability, which is crucial for real-world deployment in dynamic environments. The combination of superior performance, substantial efficiency gains, reduced reliance on domain expertise, and robust generalization makes Hierarchical DeepPruner a potentially transformative contribution to the field of combinatorial optimization, addressing long-standing scalability issues with a highly adaptable and effective approach.

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