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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 a Sebastian ORDYNIAK. Parameterized Algorithms for Modular-Width. In Gutin, Gregory and Szeider, Stefan. \textit{Parameterized and Exact Computation}. Berlin Heidelberg: Springer International Publishing, 2013, s.~163-176. ISBN~978-3-319-03897-1. Dostupné z: https://dx.doi.org/10.1007/978-3-319-03898-8\_{}15.
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