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  Reachability substitutes for planar digraphs

Katriel, I., Kutz, M., & Skutella, M.(2005). Reachability substitutes for planar digraphs (MPI-I-2005-1-002). Saarbrücken: Max-Planck-Institut für Informatik.

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MPI-I-2005-1-002.pdf (Any fulltext), 303KB
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 Creators:
Katriel, Irit1, Author           
Kutz, Martin1, Author           
Skutella, Martin1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 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.

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Language(s): eng - English
 Dates: 2005
 Publication Status: Issued
 Pages: 24 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: URI: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2005-1-002
Report Nr.: MPI-I-2005-1-002
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Title: Research Report / Max-Planck-Institut für Informatik
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