Kernels in planar digraphs

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 ( n 2 19.1 k + n 4 ) -time and O ( k 36 + 2 19.1 k k 9 + n 2 ) -time algorithms for checking whether a planar digraph D of order n has a kerne...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 71; no. 2; pp. 174 - 184
Main Authors: Gutin, Gregory, Kloks, Ton, Lee, Chuan Min, Yeo, Anders
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2005
Subjects:
Fixed-parameter complexity
Kernels
Planar digraphs
Kernels
Planar digraphs
Fixed-parameter complexity
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary: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 ( n 2 19.1 k + n 4 ) -time and O ( k 36 + 2 19.1 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.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2005.02.003