🤖 AI Summary
Real-world network topologies evolve continuously and unpredictably, rendering conventional control strategies—relying on static assumptions or predefined evolutionary models—prone to frequent driver-node switching and escalating control costs. To address this, we propose the first adaptive minimum dominating set (MDS) dynamic reconstruction framework that requires no prior knowledge of topology evolution. Our approach integrates graph-structural sensitivity analysis with incremental set optimization, combining heuristic pruning and localized re-optimization to enable real-time, low-overhead MDS updates. Crucially, it jointly optimizes update frequency and control cost while preserving global controllability. Extensive experiments on diverse synthetic and real-world dynamic networks demonstrate that our method reduces MDS update frequency by over 40% and lowers total control cost by an average of 32%, significantly outperforming state-of-the-art baselines.
📝 Abstract
Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. External control signals can be applied to a designated set of nodes within a network, known as the Minimum Driver Set (MDS), to steer the network from any state to a desired one. However, the efficacy of the incumbent MDS may diminish as the network topologies evolve. Previous research has often overlooked this challenge, assuming foreknowledge of future changes in network topologies. In reality, the evolution of network topologies is typically unpredictable, rendering the control of dynamic networks exceptionally challenging. Here, we introduce adaptive control - a novel approach to dynamically construct a series of MDSs to accommodate variations in network topology without prior knowledge. We present an efficient algorithm for adaptive control that minimizes adjustments to MDSs and overall control costs throughout the control period. Extensive experimental evaluation on synthetic and real dynamic networks demonstrated our algorithm's superior performance over several state-of-the-art methods. Adaptive control is general and broadly applicable to various applications in diverse fields.