Want to Gather? No Need to Chatter!
S\'ebastien Bouchard, Yoann Dieudonn\'e, Andrzej Pelc

TL;DR
This paper demonstrates that mobile agents can achieve gathering without communication, using only local knowledge, through two deterministic algorithms suitable for different knowledge assumptions, and extends results to leader election and gossiping.
Contribution
It introduces two novel deterministic algorithms for gathering without communication, applicable under different knowledge assumptions, and extends to leader election and gossiping.
Findings
Gathering is possible without agent communication.
Algorithms work under different knowledge assumptions about the network.
The approach also solves leader election and gossiping in the same weak model.
Abstract
A team of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node and declare that they have all met. Agents have different labels and move in synchronous rounds along links of the network. The above task is known as gathering and was traditionally considered under the assumption that when some agents are at the same node then they can talk. In this paper we ask the question of whether this ability of talking is needed for gathering. The answer turns out to be no. Our main contribution are two deterministic algorithms that always accomplish gathering in a much weaker model. We only assume that at any time an agent knows how many agents are at the node that it currently occupies but agents do not see the labels of other co-located agents and cannot exchange any information with them. They also do not see other nodes…
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