Graph Matching Optimization: A Multi-Task Framework for Addressing NP-Hard Graph Problems

A wide range of real-world data, including drug molecules, social networks, and knowledge graphs, can be effectively represented as graphs. In recent years, several NP-hard graph problems have garnered significant attention in the research community. While these problems have numerous real-world applications, their practical impact is often hindered by the high computational cost associated with solving them.

This project introduces a comprehensive approach for tackling a series of NP-hard graph problems using a multi-task framework focused on node matching. The proposed framework aims to address challenges in combining classical graph queries with advanced machine learning models. We also anticipate that the outcome of this project will shift the prevailing perception that NP-hard problems are insurmountable when inexact solutions are acceptable.

Our research plan encompasses three key tasks:

• Task 1 focuses on node-matching-based NP-hard graph problems, such as graph edit distance, maximum common subgraph, and subgraph matching. By formulating the Graph Matching Optimization (GMO) problem, which captures the common features of these problems, the framework provides a unified approach for addressing them. The task involves introducing the GMO problem, presenting the proposed multi-task framework, and exploring its application to different graph problems.

• Task 2 extends the framework to handle solution-oriented NP-hard graph problems. Unlike existing models that treat these problems as regression tasks, the proposed framework goes beyond prediction and aims to find true solutions.

• Task 3 explores the extension of the framework to NP-hard problems on a single graph, such as maximum clique and maximum independent set. The challenge lies in handling unbalanced sizes of input and target graphs.
The proposed framework offers a promising avenue for addressing NP-hard graph problems by integrating machine learning techniques and graph matching optimization. Please note that our objective is not to introduce new graph representation learning techniques. Instead, we aim to leverage advanced and suitable machine learning models to effectively tackle complex graph queries.

Overall, this project presents a comprehensive plan for tackling NP-hard graph problems through a multi-task framework. By combining innovative techniques, efficient algorithms, and advanced machine learning models, the proposed approach has the potential to revolutionize graph query processing and pave the way for new breakthroughs in graph theory and algorithms.