At a Glance
A simple leader‑and‑followers scheme using only short‑range messages lets hundreds of agents navigate unknown maze‑like graphs to a hidden goal with provable safety (no collisions) and time performance that approaches an optimal strategy that knows the map in advance.
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Key Findings
A single active agent (the head) runs a normal single‑agent maze solver while all other agents form a tree of followers that track and compete for the head’s previous positions. Local directed messages (along one chosen corridor) and short broadcast signals resolve conflicts so agents never collide and remain connected. The algorithm is complete (guarantees all agents reach the goal) and the total finish time scales asymptotically like an optimal full‑knowledge solution. Simulations up to 625 agents show lower per‑agent travel (fuel) as agent count grows, outperforming a baseline where every agent runs the single‑agent solver independently agent-to-agent protocol.
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Data Highlights
1Validated in simulation with up to 625 agents.
2Algorithm guarantees exactly one head at every time step (single active searcher).
3Algorithm prevents collisions: at most one active agent occupies any non-goal node at any time (no vertex or following conflicts).
What This Means
Engineers building multi-robot exploration or inspection systems (pipes, caves, buildings) who need scalable, collision‑free coordination with only local communication. Technical leads designing distributed agent orchestration or safety nets can use the provable guarantees to simplify coordination and reduce per‑robot travel costs. Researchers in distributed planning will find a proofed recipe that bridges single‑agent search and fully decentralized group behavior Role-Based Agent Pattern.
Key Figures
Fig 3: Figure 3: Simulations in grid mazes using Trémaux’s algorithm and BFS at times k = 20 k=20 and k = 100 k=100 . Walls are dark gray, and nodes that were already visited are light gray. In this example, Trémaux’s algorithm explores a larger portion of the graph, though BFS is the first to reach the goal.
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Learn MoreConsiderations
Relies on synchronous time steps, a fixed activation order, and the start node being a leaf; those assumptions may not match all real deployments. Communication is modeled as two‑hop and cannot pass through occupied nodes, so message loss, delays, or lossy wireless links could break the guarantees. Theoretical results are asymptotic (scale with many agents) and experiments are simulation‑based; real‑world factors like sensor noise and uneven agent dynamics were not evaluated here. Guardrails
The Details
Agents start together at a leaf start node. One active agent — the head — runs a standard single‑agent maze solver step by step; every other active agent picks one leader to follow so that the leader graph is always a tree rooted at the head. Agents exchange three lightweight message types each step: a status broadcast (ID, leader pointer, goal flag), a competing flag (if a follower plans to move), and a head message (head’s planned move and whether it transfers head role). After moving, agents send a directed cast along the corridor they just left, letting followers know which node became free. A deterministic selector picks a single winner among agents competing for the same node, preserving collision avoidance and connectivity. A link to LLM-as-Judge Pattern is noted as a potential approach for evaluating such decentralized strategies. Formal proofs show there is always exactly one head, first visit to any node (except start) is by the head, and no vertex or following conflicts occur (so collisions cannot happen). Makespan (time until all agents reach the goal) is proven to be asymptotically equivalent, as agent count grows, to an optimal strategy that has full map knowledge. Simulation tests (up to 625 agents) indicate average travel per agent decreases with more agents and that the method beats a naive baseline where every agent runs the single‑agent solver independently — making it practical for large swarms that must find a hidden goal with only local, short‑range communication.
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Credibility Assessment:
All authors show very low h-indices, no affiliations listed, arXiv only, and zero citations — limited reputational signals.