Monotone Decontamination of Arbitrary Dynamic Graphs with Mobile Agents

TL;DR

This paper investigates the problem of monotone network decontamination using mobile agents in arbitrary dynamic graphs, proposing models, bounds, and strategies to optimize agent usage under dynamic conditions.

Contribution

It introduces two models of dynamic graphs for monotone decontamination and provides bounds and strategies to minimize the number of agents needed.

Findings

Established lower and upper bounds on agent numbers for decontamination

Highlighted challenges due to edge disappearance and reappearance

Proposed models for dynamic graph decontamination

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.