COMBHelper: A Neural Approach to Reduce Search Space for Graph Combinatorial Problems

TL;DR

COMBHelper employs a neural network to effectively prune the search space in graph-based combinatorial optimization problems, significantly enhancing the efficiency of traditional algorithms.

Contribution

It introduces a novel GNN-based method with knowledge distillation and boosting modules to reduce search space and improve solution efficiency in NP-hard graph problems.

Findings

At least 2x speedup over traditional algorithms

Effective node selection improves search efficiency

Neural pruning maintains solution quality

Abstract

Combinatorial Optimization (CO) problems over graphs appear routinely in many applications such as in optimizing traffic, viral marketing in social networks, and matching for job allocation. Due to their combinatorial nature, these problems are often NP-hard. Existing approximation algorithms and heuristics rely on the search space to find the solutions and become time-consuming when this space is large. In this paper, we design a neural method called COMBHelper to reduce this space and thus improve the efficiency of the traditional CO algorithms based on node selection. Specifically, it employs a Graph Neural Network (GNN) to identify promising nodes for the solution set. This pruned search space is then fed to the traditional CO algorithms. COMBHelper also uses a Knowledge Distillation (KD) module and a problem-specific boosting module to bring further efficiency and efficacy. Our extensive experiments show that the traditional CO algorithms with COMBHelper are at least 2 times faster than their original versions.