Connectivity maintenance against link uncertainty and heterogeneity in adversarial networks

Abstract

This paper delves into the challenge of maintaining connectivity in adversarial networks, focusing on the preservation of essential links to prevent the disintegration of network components under attack. Unlike previous approaches that assume a stable and homogeneous network topology, this study introduces a more realistic model that incorporates both link uncertainty and heterogeneity. Link uncertainty necessitates additional probing to confirm link existence, while heterogeneity reflects the varying resilience of links against attacks. We model the network as a random graph where each link is defined by its existence probability, probing cost, and resilience. The primary objective is to devise a defensive strategy that maximizes the expected size of the largest connected component at the end of an adversarial process while minimizing the probing cost, irrespective of the attack patterns employed. We begin by establishing the NP-hardness of the problem and then introduce an optimal defensive strategy based on dynamic programming. Due to the high computational cost of achieving optimality, we also develop two approximate strategies that offer efficient solutions within polynomial time. The first is a heuristic method that assesses link importance across three heterogeneous subnetworks, and the second is an adaptive minimax policy designed to minimize the defender’s potential worst-case loss, with guaranteed performance. Through extensive testing on both synthetic and real-world datasets across various attack scenarios, our strategies demonstrate significant advantages over existing methods.