Abstract
A swarm of mobile agents starting at the root of a tree has to explore it: every node of the tree has to be visited by at least one agent. In every round, each agent can remain idle or move to an adjacent node. In any round all agents have to be at distance at most d, where d is a parameter called the range of the swarm. The goal is to explore the tree as fast as possible.
If the topology of the tree is known to the agents, we establish optimal exploration time for any range d and give an optimal exploration algorithm. The formula for the optimal exploration time of a tree by a swarm of agents depends on the range of the swarm and on the characteristics of the tree. If the tree is unknown, the quality of an exploration algorithm \(\mathcal{A}\) is measured by comparing its time to that of the optimal algorithm having full knowledge of the tree. The ratio between these times, maximized over all starting nodes and over all trees, is called the overhead of algorithm \(\mathcal{A}\). Overhead 2 is achieved when the swarm executes a DFS, remaining together all the time. We show that this overhead cannot be improved, for any range d.
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Czyzowicz, J., Pelc, A., Roy, M. (2012). Tree Exploration by a Swarm of Mobile Agents. In: Baldoni, R., Flocchini, P., Binoy, R. (eds) Principles of Distributed Systems. OPODIS 2012. Lecture Notes in Computer Science, vol 7702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35476-2_9
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DOI: https://doi.org/10.1007/978-3-642-35476-2_9
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