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  Exploring unknown environments

Albers, S., & Henzinger, M. R.(1997). Exploring unknown environments (MPI-I-1997-1-017). Saarbrücken: Max-Planck-Institut für Informatik.

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 Creators:
Albers, Susanne1, Author              
Henzinger, Monika R.2, Author
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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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~\cite{K} gave a lower bound for $R$ of $\Omega(d^2 m)$, and Deng and Papadimitriou~\cite{DP} 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 $d^{\Omega(\log d)}m$ for our algorithm. Additionally, we give lower bounds of $2^{\Omega(d)}m$, resp.\ $d^{\Omega(\log d)}m$ for various other natural exploration algorithms.

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Language(s): eng - English
 Dates: 1997
 Publication Status: Published in print
 Pages: 23 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: Report Nr.: MPI-I-1997-1-017
BibTex Citekey: AlbersHenzinger97
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Title: Research Report / Max-Planck-Institut für Informatik
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