Abstract
We consider a tree which has to be completely explored by a group of k robots, initially placed at the root. The robots are mobile and can communicate using radio devices, but the communication range is bounded. They decide based on local, partial knowledge, and exchange information gathered during the exploration. There is no central authority which knows the graph and could control the movements of the robots – they have to organize themselves and jointly explore the tree.
The problem is that at every point of time the remaining unknown part of the tree may appear to be the worst case setting for the current deployment of robots. We present a deterministic distributed algorithm to explore T and we use a parameter of a tree called density. We compare the performance of our algorithm with the optimal algorithm having a-priori knowledge of the same tree. We show that the above ratio is influenced only by the density and the height of the tree. Since the competitive ratio does not depend on the number of robots, our algorithm truly emphasizes the phenomena of self-organization. The more robots are provided, the faster the exploration of the terrain is completed.
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 the EU within the 6th Framework Programme under contract 001907 (DELIS).
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References
Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press, New York (1998)
Rao, N., Kareti, S., Shi, W., Iyenagar, S.: Robot navigation in unknown terrains: Introductory survey of non-heuristic algorithms. Technical Report ORNL/TM-12410 (1993)
Frederickson, G., Hecht, M., Kim, C.: Approximation algorithms for some routing problems. SIAM Journal on Computing 7, 178–193 (1978)
Averbakh, I., Berman, O.: Minmax p-traveling salesmen location problems on a tree. Annals of Operations Research 110, 55–68 (2002)
Dynia, M., Korzeniowski, M., Schindelhauer, C.: Power-aware collective tree exploration. In: Grass, W., Sick, B., Waldschmidt, K. (eds.) ARCS 2006. LNCS, vol. 3894, pp. 341–351. Springer, Heidelberg (2006)
Even, G., Garg, N., Könemann, J., Ravi, R., Sinha, A.: Min-max tree covers of graphs. Operations Research Letters 32, 309–315 (2004)
Averbakh, I., Berman, O.: (p - 1)/(p + 1)-approximate algorithms for p-traveling salesmen problems on a tree with minmax objective. Discrete Applied Mathematics 75, 201–216 (1997)
Averbakh, I., Berman, O.: A heuristic with worst-case analysis for minimax routing of two traveling salesmen on a tree. Discrete Applied Mathematics 68, 17–32 (1996)
Bender, M., Slonim, D.: The power of team exploration: two robots can learn unlabeled directed graphs. In: Proc. FOCS 1994, pp. 75–85 (1994)
Bender, M., Fernández, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: exploring and mapping directed graphs. In: Proc. 30th Symp. Theory of Computing, pp. 269–278. ACM, New York (1998)
Panaite, P., Pelc, A.: Exploring unknown undirected graphs. In: SODA 1998: Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, pp. 316–322. Society for Industrial and Applied Mathematics, Philadelphia (1998)
Awerbuch, B., Betke, M., Rivest, R., Singh, M.: Piecemeal graph exploration by a mobile robot. Information and Computation 152, 155–172 (1999)
Dessmark, A., Pelc, A.: Optimal graph exploration without good maps. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 374–386. Springer, Heidelberg (2002)
Fleischer, R., Trippen, G.: Exploring an unknown graph efficiently. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 11–22. Springer, Heidelberg (2005)
Fraigniaud, P., Gąsieniec, L., Kowalski, D.R., Pelc, A.: Collective tree exploration. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 141–151. Springer, Heidelberg (2004)
Fraigniaud, P., Ilcinkas, D., Rajsbaum, S., Tixeuil, S.: Space lower bounds for graph exploration via reduced automata. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 140–154. Springer, Heidelberg (2005)
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Dynia, M., Kutyłowski, J., der Heide, F.M.a., Schindelhauer, C. (2006). Smart Robot Teams Exploring Sparse Trees. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_29
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DOI: https://doi.org/10.1007/11821069_29
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