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Exploring unknown environments

Albers, Susanne and Henzinger, Monika R.

MPI-I-97-1-017. July 1997, 23 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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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  AUTHOR = {Albers, Susanne and Henzinger, Monika R.},
  TITLE = {Exploring unknown environments},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-97-1-017},
  MONTH = {July},
  YEAR = {1997},
  ISSN = {0946-011X},