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Collaborative Exploration of Trees by Energy-Constrained Mobile Robots

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Abstract

We study the problem of exploration of a tree by mobile agents (robots) that have limited energy. The energy constraint bounds the number of edges that can be traversed by a single agent. We use a team of agents to collectively explore the tree and the objective is to minimize the size of this team. The agents start at a single node, the designated root of the tree and the height of the tree is assumed to be less than the energy bound B of the agents. The agents have local vision and communication capabilities; two agents can exchange information only when they are collocated at the same node. We provide an exploration algorithm for visiting all nodes of the unknown tree and we compare our algorithm with the optimal offline algorithm that has complete knowledge of the tree. Our algorithm has a competitive ratio of O(log B), independent of the number of nodes in the tree. We also show that this is the best possible competitive ratio for exploration of unknown trees.

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Notes

  1. Note that the only way to store information at a node is by having an agent stay at the node carrying this information.

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Acknowledgements

This work was partially supported by the ANR projects MACARON (anr-13-js02-0002) and ANCOR (anr-14-CE36-0002-01), and by the Polish National Science Center grant DEC-2011/02/A/ST6/00201. The second author would like to thank Krzysztof Kwaśniewski for interesting discussions on the subject.

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Authors and Affiliations

  1. Aix-Marseille University, CNRS, LIF, Marseille, France

    Shantanu Das & Christina Karousatou

  2. Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Gdańsk, Poland

    Dariusz Dereniowski

Authors
  1. Shantanu Das
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  2. Dariusz Dereniowski
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  3. Christina Karousatou
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Correspondence to Shantanu Das.

Additional information

Some of the results of this paper have been presented at the 22nd Colloquium on Structural Information and Communication Complexity (SIROCCO), Spain 2015 [11].

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Das, S., Dereniowski, D. & Karousatou, C. Collaborative Exploration of Trees by Energy-Constrained Mobile Robots. Theory Comput Syst 62, 1223–1240 (2018). https://doi.org/10.1007/s00224-017-9816-3

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  • DOI: https://doi.org/10.1007/s00224-017-9816-3

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