Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems

TL;DR

This paper introduces a machine learning framework that reduces search space and enhances solvers for complex subset enumeration problems, demonstrated on maximum clique listing in large real-world networks, achieving significant speedups.

Contribution

The paper presents a novel machine learning approach to prune search spaces and improve solver efficiency for NP-hard subset problems, specifically applied to maximum clique enumeration.

Findings

Retains all optimal solutions in large networks

Achieves several fold speedups of existing algorithms

Demonstrates scalability and robustness of the approach

Abstract

We propose a simple, powerful, and flexible machine learning framework for (i) reducing the search space of computationally difficult enumeration variants of subset problems and (ii) augmenting existing state-of-the-art solvers with informative cues arising from the input distribution. We instantiate our framework for the problem of listing all maximum cliques in a graph, a central problem in network analysis, data mining, and computational biology. We demonstrate the practicality of our approach on real-world networks with millions of vertices and edges by not only retaining all optimal solutions, but also aggressively pruning the input instance size resulting in several fold speedups of state-of-the-art algorithms. Finally, we explore the limits of scalability and robustness of our proposed framework, suggesting that supervised learning is viable for tackling NP-hard problems in practice.