de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Report

Exploring unknown environments

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons43989

Albers,  Susanne
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

1997-1-017
(Any fulltext), 10KB

Supplementary Material (public)
There is no public supplementary material available
Citation

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


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-9D82-5
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.