@techreport{,
TITLE = {Reachability substitutes for planar digraphs},
AUTHOR = {Katriel, Irit and Kutz, Martin and Skutella, Martin},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2005-1-002},
NUMBER = {MPI-I-2005-1-002},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {2005},
DATE = {2005},
ABSTRACT = {Given a digraph $G = (V,E)$ with a set $U$ of vertices marked ``interesting,'' we want to find a smaller digraph $\RS{} = (V',E')$ with $V' \supseteq U$ in such a way that the reachabilities amongst those interesting vertices in $G$ and \RS{} are the same. So with respect to the reachability relations within $U$, the digraph \RS{} is a substitute for $G$. We show that while almost all graphs do not have reachability substitutes smaller than $\Ohmega(|U|^2/\log |U|)$, every planar graph has a reachability substitute of size $\Oh(|U| \log^2 |U|)$. Our result rests on two new structural results for planar dags, a separation procedure and a reachability theorem, which might be of independent interest.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}