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@inproceedings{1159488,
author = {Gajarský, Jakub and Lampis, Michael and Ordyniak, Sebastian},
address = {Berlin Heidelberg},
booktitle = {Parameterized and Exact Computation},
doi = {http://dx.doi.org/10.1007/978-3-319-03898-8_15},
editor = {Gutin, Gregory and Szeider, Stefan},
keywords = {parameterized complexity; modular width; shrub depth; chromatic number; hamiltonian path},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin Heidelberg},
isbn = {978-3-319-03897-1},
pages = {163-176},
publisher = {Springer International Publishing},
title = {Parameterized Algorithms for Modular-Width},
year = {2013}
}
TY - JOUR
ID - 1159488
AU - Gajarský, Jakub - Lampis, Michael - Ordyniak, Sebastian
PY - 2013
TI - Parameterized Algorithms for Modular-Width
PB - Springer International Publishing
CY - Berlin Heidelberg
SN - 9783319038971
KW - parameterized complexity
KW - modular width
KW - shrub depth
KW - chromatic number
KW - hamiltonian path
N2 - It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as possible, covers dense graphs but does not incur such a heavy algorithmic penalty. The main contribution of this paper is to consider a parameter called modular-width, defined using the well-known notion of modular decompositions. Using a combination of ILP and dynamic programming we manage to design FPT algorithms for Coloring and Partitioning into paths (and hence Hamiltonian path and Hamiltonian cycle), which are W-hard for both clique-width and its recently introduced restriction, shrub-depth. We thus argue that modular-width occupies a sweet spot as a graph parameter, generalizing several simpler notions on dense graphs but still evading the “price of generality” paid by clique-width.
ER -
GAJARSKÝ, Jakub, Michael LAMPIS and Sebastian ORDYNIAK. Parameterized Algorithms for Modular-Width. In Gutin, Gregory and Szeider, Stefan. \textit{Parameterized and Exact Computation}. Berlin Heidelberg: Springer International Publishing. p.~163-176. ISBN~978-3-319-03897-1. doi:10.1007/978-3-319-03898-8\_{}15. 2013.
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