Abstract
A large group of autonomous, mobile entities e.g. robots initially placed at some arbitrary node of the graph has to jointly visit all nodes (not necessarily all edges) and finally return to the initial position. The graph is not known in advance (an online setting) and robots have to traverse an edge in order to discover new parts (edges) of the graph. The team can locally exchange information, using wireless communication devices.
We compare a cost of the online and optimal offline algorithm which knows the graph beforehand (competitive ratio). If the cost is the total time of an exploration, we prove the lower bound of Ω(logk /loglogk) for competitive ratio of any deterministic algorithm (using global communication). This significantly improves the best known constant lower bound. For the cost being the maximal number of edges traversed by a robot (the energy) we present an improved (4 − 2/k)-competitive online algorithm for trees.
This research is partially supported by the DFG-Sonderforschungsbereich SPP 1183: ”Organic Computing. Smart Teams: Local, Distributed Strategies for Self-Organizing Robotic Exploration Teams” and by MNiSW grant number N206 001 31/0436, 2006-2008.
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Dynia, M., Łopuszański, J., Schindelhauer, C. (2007). Why Robots Need Maps. In: Prencipe, G., Zaks, S. (eds) Structural Information and Communication Complexity. SIROCCO 2007. Lecture Notes in Computer Science, vol 4474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72951-8_5
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DOI: https://doi.org/10.1007/978-3-540-72951-8_5
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