An Incremental Evaluation Mechanism for the Critical Node Problem

TL;DR

This paper introduces an efficient incremental evaluation mechanism for the Critical Node Problem, significantly reducing computation time during local search and improving solution quality in benchmark tests.

Contribution

The paper proposes a novel incremental evaluation mechanism (IEM) that accelerates objective function computation in CNP, enhancing existing algorithms' efficiency and effectiveness.

Findings

IEM reduces the complexity of objective function evaluation.

Applying IEM improves the performance of greedy algorithms.

Experimental results outperform state-of-the-art methods.

Abstract

The Critical Node Problem (CNP) is to identify a subset of nodes in a graph whose removal maximally degrades pairwise connectivity. The CNP is an important variant of the Critical Node Detection Problem (CNDP) with wide applications. Due to its NP-hardness for general graphs, most works focus on local search algorithms that can return a good quality solution in a reasonable time. However, computing the objective function of CNP is a frequent procedure and is time-consuming (with complexity O(|V | + |E|)) during the search, which is a common problem that previous algorithms suffered from. In this paper, we propose a general incremental evaluation mechanism (IEM) to compute the objective function with much lower complexity. In this work, we improved two important greedy operations with IEM, along with experiments. Finally, we evaluate IEM by applying it into an evolutionary algorithm on two popular benchmarks, compared with the state-of-the-art approach. The experimental results showed the significance of IEM.