Hybrid Learning with New Value Function for the Maximum Common Subgraph Problem

TL;DR

This paper introduces a novel hybrid learning approach with a new value function for the Maximum Common Subgraph problem, significantly enhancing branch-and-bound algorithm performance through reinforcement learning.

Contribution

It proposes a new value function and hybrid selection strategy within a BnB algorithm, improving efficiency over existing methods for MCS.

Findings

McSplitDAL outperforms current best BnB algorithms

The new value function enhances vertex selection effectiveness

Hybrid strategy improves overall algorithm efficiency

Abstract

Maximum Common induced Subgraph (MCS) is an important NP-hard problem with wide real-world applications. Branch-and-Bound (BnB) is the basis of a class of efficient algorithms for MCS, consisting in successively selecting vertices to match and pruning when it is discovered that a solution better than the best solution found so far does not exist. The method of selecting the vertices to match is essential for the performance of BnB. In this paper, we propose a new value function and a hybrid selection strategy used in reinforcement learning to define a new vertex selection method, and propose a new BnB algorithm, called McSplitDAL, for MCS. Extensive experiments show that McSplitDAL significantly improves the current best BnB algorithms, McSplit+LL and McSplit+RL. An empirical analysis is also performed to illustrate why the new value function and the hybrid selection strategy are effective.