PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Kernels in planar digraphs
Gregory Gutin, Ton KLoks, Chuan Min Lee and Anders Yeo
Journal of Computer and System Sciences Volume 71, pp. 174-184, 2005.


A set $S$ of vertices in a digraph $D=(V,A)$ is a kernel if $S$ is independent and every vertex in $V-S$ has an out-neighbor in $S$. We show that there exist $O(n2^{19.1 \sqrt{k}}+n^4)$-time and $O(k^{36}+2^{19.1 \sqrt{k}} k^9 + n^2)$-time algorithms for checking whether a planar digraph $D$ of order $n$ has a kernel with at most $k$ vertices. Moreover, if $D$ has a kernel of size at most $k$, the algorithms find such a kernel of minimal size.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:221
Deposited By:Gregory Gutin
Deposited On:22 December 2004