Abstract

The distance-based critical node problem involves identifying a subset of nodes in a network whose removal minimises a pre-defined distance-based connectivity measure. Having the classical critical node problem as a special case, the distance-based critical node problem is computationally challenging. In this article, we study the distance-based critical node problem from a heuristic algorithm perspective. We consider the distance-based connectivity objective whose goal is to minimise the number of node pairs connected by a path of length at most k, subject to budgetary constraints. We propose a centrality based heuristic which combines a backbone-based crossover procedure to generate good offspring solutions and a centrality-based neighbourhood search to improve the solution. Extensive computational experiments on real-world and synthetic graphs show the effectiveness of the developed heuristic in generating good solutions when compared to exact solution. Our empirical results also provide useful insights for future algorithm development.

摘要

基于距离的关键节点问题涉及识别网络中的节点子集，这些节点的移除最小化了预定义的基于距离的连通性度量。将经典的关键节点问题作为特例，基于距离的关键节点问题在计算上具有挑战性。在本文中，我们从启发式算法的角度研究了基于距离的关键节点问题。我们考虑基于距离的连接目标，其目标是最小化由长度最多为k的路径连接的节点对的数量，受预算限制。我们提出了一种基于中心性的启发式算法，它结合了基于骨干的交叉过程来生成良好的后代解决方案和基于中心性的邻域搜索来改进解决方案。对真实世界和合成图的广泛计算实验表明，与精确解决方案相比，所开发的启发式算法在生成良好解决方案方面的有效性。我们的实证结果也为未来的算法开发提供了有用的见解。