Semi-Synchronous Exploration in Dynamic Graphs

2026-05-14

AI Summary

This study addresses the problem of graph exploration by multiple agents in 1-interval-connected dynamic graphs under an adversarial semi-synchronous scheduler, where the topology changes arbitrarily, edge ports are dynamically relabeled, and the adversary may deactivate a subset of agents in each round. Through a combination of combinatorial analysis and distributed algorithm design, the work establishes the first tight impossibility bound: exploration is infeasible whenever the adversary deactivates at least ⌈k/(n−2)⌉−1 agents per round. Conversely, if the number of deactivated agents per round is at most ⌈k/(n−2)⌉−2 and agents possess one-hop visibility and one-hop communication capabilities, a deterministic exploration algorithm exists. This result precisely characterizes the trade-off between adversarial deactivation power and agent capabilities in dynamic graph exploration.

Abstract

We study the fundamental problem of graph exploration in dynamic graphs using mobile agents. We consider $1$-interval connected dynamic graphs, where the topology may change arbitrarily from round to round as long as the graph remains connected, and edges are assigned with the dynamic port labeling at each round. The execution follows a semi-synchronous scheduler, under which an adversary may deactivate an arbitrary subset of agents in each round. For a graph with $n$ nodes and $k$ agents, we show that exploration is impossible if the adversary can deactivate at least $ \left\lceil \frac{k}{n-2} \right\rceil - 1$ agents per round, even when agents are equipped with unbounded memory, have global communication and full visibility. This yields an upper bound, implying that exploration is solvable only when the adversary deactivates at most $\left\lceil \frac{k}{n-2} \right\rceil - 2$ agents per round. We further establish that achieving exploration at this threshold requires agents to have both $1$-hop visibility and $1$-hop communication. Finally, we present the exploration algorithm using $k$ agents when the adversary deactivates at most $ \left\lceil \frac{k}{n-2} \right\rceil - 2$ agents, assuming agents are equipped with $1$-hop visibility and global communication, and matches the adversarial deactivation bound implied by the impossibility results.

Problem

• dynamic graphs
• graph exploration
• mobile agents
• semi-synchronous scheduler
• adversarial deactivation

Innovation

• dynamic graphs
• semi-synchronous scheduler
• mobile agents
• graph exploration
• adversarial deactivation