Optimizing Minimum Vertex Cover Solving via a GCN-assisted Heuristic Algorithm

TL;DR

Elsarticle.cls provides a robust LaTeX class tailored for Elsevier journal submissions, built to minimize package conflicts while supporting common tools and formats. It emphasizes broad compatibility by integrating standard packages such as natbib and hyperref and by offering flexible frontmatter and formatting options. The paper outlines installation workflows via CTAN and Elsevier resources, including an installer-based generation of the cls file and necessary TEXMF updates. Overall, the class aims to simplify producing publication-ready manuscripts with consistent styling across diverse LaTeX environments.

Abstract

The problem of finding a minimum vertex cover (MVC) in a graph is a well-known NP-hard problem with significant practical applications in optimization and scheduling. Its complexity, combined with the increasing scale of problems, underscores the need for efficient and effective algorithms. However, existing heuristic algorithms for MVC often rely on simplistic initialization strategies and overlook the impact of edge attributes and neighborhood information on vertex selection. In this paper, we introduce GCNIVC, a novel heuristic search algorithm designed to address the limitations of existing methods for solving MVC problems in large-scale graphs. Our approach features two main innovations. First, it utilizes a Graph Convolutional Network (GCN) to capture the global structure of graphs, which enables the generation of high-quality initial solutions that enhance the efficiency of the subsequent search process. Second, GCNIVC introduces a new heuristic that employs three containers and the concept of double-covered edges (dc-edges), improving search efficiency and providing greater flexibility for adding and removing operations based on edge attributes. Through extensive experiments on benchmark datasets, we demonstrate that GCNIVC outperforms state-of-the-art MVC algorithms in terms of both accuracy and efficiency. Our results highlight the effectiveness of GCNIVC's GCN-assisted initialization and its edge-informed search strategy. This study not only advances the understanding of MVC problem-solving but also contributes a new tool for addressing large-scale graph optimization challenges.