Exploring unknown environments (1997) [61 citations — 3 self]
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@INPROCEEDINGS{Albers97exploringunknown,author = {Susanne Albers and Monika R. Henzinger},
title = {Exploring unknown environments},
booktitle = {SIAM Journal on Computing},
year = {1997},
pages = {416--425}
}
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Abstract:
We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum number R of edge traversals. Koutsoupias [12] gave a lower bound for R of \Omega\Gamma d 2 m), and Deng and Papadimitriou [9] showed an upper bound of d O(d) m, where m is the number edges in the graph and d is the minimum number of edges that have to be added to make the graph Eulerian. We give the first sub-exponential algorithm for this exploration problem, which achieves an upper bound of d O(log d) m. We also show a matching lower bound of d\Omega\Gamma207 d) m for our algorithm. Additionally, we give lower bounds of 2 \Omega\Gamma d) m, resp. d \Omega\Gamma828 d) m for various other natural exploration algorithms.
