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Maximum k vertex cover problem is a significant combinatorial optimization problem with various applications, such as transportation planning, social networks and sensor placement. Up to now, no practical algorithm has ever been proposed to solve this problem. Therefore, this paper aims to present an efficient local search algorithm LSKVC combining three methods for it.

First, the quick incremental evaluation method is proposed to update the related vertex scores following each addition or removal incrementally rather than recalculating them, which can speed up the algorithm. Second, the configuration checking method forbids vertices whose configuration has not changed since the last removal from being added into the candidate solution again, which can avoid the cycling problem effectively. Third, the two-stage exchange method swaps the pairs of inside and outside vertices separately rather than simultaneously, which can guarantee the tradeoff between the accuracy and complexity of the algorithm.

The proposed algorithm LSKVC is compared with the traditional GRASP algorithm and the well-known commercial solver CPLEX on DIMACS and BHOSLIB benchmarks. For the best solutions, the LSKVC algorithm is significantly superior to GRASP and CPLEX on DIMACS instances and the CPLEX solver fails, and the LSKVC algorithm slightly outperforms GRASP on the BHOSLIB instances. In addition, we undertake comparative studies of the offered methodologies and demonstrate their efficacy.

In previous research, the focus on the maximum k-vertex cover problem primarily centered around exact algorithms and approximation algorithms, with limited application of heuristic algorithms. While heuristic algorithms have been well-explored for the closely related Minimum Vertex Cover problem, they have seen limited application in the context of the maximum k-vertex cover problem. Consequently, existing algorithms designed for the Minimum Vertex Cover problem do not exhibit satisfactory performance when applied to the maximum k-vertex cover problem. In response to this challenge, we have undertaken algorithmic improvements specifically tailored to address this issue.

The purpose of this paper is to examine the influence of intelligent manufacturing on audit quality and its underlying mechanism as well as the variation in this influence across different types of organizations.

This research utilizes a difference-in-differences (DID) method to examine how enterprises that apply intelligent manufacturing choose auditors and impact their audit work. The study is based on 15,228 observations of Chinese-listed A-shares from 2011 to 2020.

(1) There is a strong correlation between intelligent manufacturing and audit quality. (2) This positive correlation is statistically significant only in state-owned enterprises (SOEs), those that have steady institutional investors and where the roles of the CEO and chairman are distinct. (3) Enterprises that have implemented intelligent manufacturing are more inclined to employ auditors who possess extensive industry expertise. The auditor's industry expertise plays a crucial role in ensuring audit quality. (4) The adoption of intelligent manufacturing also leads to higher audit fees and longer audit delay periods.

This paper validates the beneficial impact of intelligent manufacturing on improving corporate governance. In addition, it is recommended that managers prioritize the involvement of skilled auditors with specialized knowledge in the industry to ensure the high audit quality and the transparency of information in intelligent manufacturing enterprises.

This study builds upon previous research that has shown the importance of artificial intelligence in enhancing audit procedures. It contributes to the existing body of knowledge by examining how enterprise intelligent manufacturing systems (IMS) enhance audit quality. Additionally, this study provides valuable information on how to improve audit quality in the field of intelligent manufacturing by strategically selecting auditors based on resource dependency theory.