Abstract
A robot has to visit all nodes and traverse all edges of an unknown undirected connected graph, using as few edge traversals as possible. The quality of an exploration algorithm A is measured by comparing its cost (number of edge traversals) to that of the optimal algorithm having full knowledge of the graph. The ratio between these costs, maximized over all starting nodes in the graph and over all graphs in a given class U, is called the overhead of algorithm A for the class U of graphs. We construct natural exploration algorithms, for various classes of graphs, that have smallest, or — in one case — close to smallest, overhead. An important contribution of this paper is establishing lower bounds that prove optimality of these exploration algorithms.
This research was done during a visit of Anders Dessmark at the Université du Québec à Hull.
Andrzej Pelc was supported in part by NSERC grant OGP 0008136.
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References
S. Albers and M. R. Henzinger, Exploring unknown environments, SIAM Journal on Computing 29 (2000), 1164–1188.
B. Awerbuch, M. Betke, R. Rivest and M. Singh, Piecemeal graph learning by a mobile robot, Proc. 8th Conf. on Comput. Learning Theory (1995), 321–328.
E. Bar-Eli, P. Berman, A. Fiat and R. Yan, On-line navigation in a room, Journal of Algorithms 17 (1994), 319–341.
M.A. Bender, A. Fernandez, D. Ron, A. Sahai and S. Vadhan, The power of a pebble: Exploring and mapping directed graphs, STOC’98, 269–278.
M.A. Bender and D. Slonim, The power of team exploration: Two robots can learn unlabeled directed graphs, FOCS’94, 75–85.
A. Blum, P. Raghavan and B. Schieber, Navigating in unfamiliar geometric terrain, SIAM Journal on Computing 26 (1997), 110–137.
M. Betke, R. Rivest and M. Singh, Piecemeal learning of an unknown environment, Machine Learning 18 (1995), 231–254.
X. Deng, T. Kameda and C.H. Papadimitriou, How to learn an unknown environment I: the rectilinear case, Journal of the ACM 45 (1998), 215–245.
X. Deng and C. H. Papadimitriou, Exploring an unknown graph, Journal of Graph Theory 32 (1999), 265–297.
K. Diks, P. Fraigniaud, E. Kranakis, A. Pelc, Tree exploration with little memory, SODA’2002, San Francisco, U. S.A., January 2002.
C.A. Duncan, S.G. Kobourov and V. S.A. Kumar, Optimal constrained graph exploration, SODA’2001, 807–814.
P. Panaite and A. Pelc, Exploring unknown undirected graphs, Journal of Algorithms 33 (1999), 281–295.
P. Panaite, A. Pelc, Impact of topographic information on graph exploration efficiency, Networks, 36 (2000), 96–103.
N. S.V. Rao, S. Hareti, W. Shi and S. S. Iyengar, Robot navigation in unknown terrains: Introductory survey of non-heuristic algorithms, Tech. Report ORNL/TM-12410, Oak Ridge National Laboratory, July 1993.
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Dessmark, A., Pelc, A. (2002). Optimal Graph Exploration without Good Maps. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_35
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DOI: https://doi.org/10.1007/3-540-45749-6_35
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