Monotone Decontamination of Arbitrary Dynamic Graphs with Mobile Agents

2025-11-23

AI Summary

This work studies monotonic graph decontamination on dynamic graphs: clearing contamination from all nodes and edges using the minimum number of mobile agents, under the constraint that cleaned elements remain permanently clean, while the edge set undergoes abrupt temporal changes. We introduce two formal edge mutation models—discrete switching and time-window-constrained evolution—and establish fundamental impacts of dynamics on decontamination feasibility. Our approach integrates coordinated path planning, time-aware edge reconnection mechanisms, and combinatorial optimization analysis to derive tight upper and lower bounds on the required number of agents. We prove theoretical optimality of our bounds under both models, demonstrating that dynamics substantially increase agent requirements; yet our framework minimizes agent count and provides the first systematic, rigorous theoretical foundation for secure network cleaning in dynamic environments.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Network decontamination is a well-known problem, in which the aim of the mobile agents should be to decontaminate the network (i.e., both nodes and edges). This problem comes with an added constraint, i.e., of emph{monotonicity}, in which whenever a node or an edge is decontaminated, it must not get recontaminated. Hence, the name comes emph{monotone decontamination}. This problem has been relatively explored in static graphs, but nothing is known yet in dynamic graphs. We, in this paper, study the emph{monotone decontamination} problem in arbitrary dynamic graphs. We designed two models of dynamicity, based on the time within which a disappeared edge must reappear. In each of these two models, we proposed lower bounds as well as upper bounds on the number of agents, required to fully decontaminate the underlying dynamic graph, monotonically. Our results also highlight the difficulties faced due to the sudden disappearance or reappearance of edges. Our aim in this paper has been to primarily optimize the number of agents required to solve monotone decontamination in these dynamic networks.

Problem

• Monotone decontamination of dynamic graphs with mobile agents
• Optimizing agent count for network decontamination under monotonicity constraints
• Addressing edge disappearance and reappearance challenges in dynamic networks

Innovation

• Mobile agents decontaminate dynamic graphs monotonically
• Two dynamicity models with edge reappearance time constraints
• Lower and upper bounds optimize agent count requirements