Parameterized Algorithms for Modular-Width

DOI10.1007/978-3-319-03898-8_15zbMATH Open1406.68080arXiv1308.2858OpenAlexW2962759123MaRDI QIDQ2867081

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Publication date: 10 December 2013

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Abstract: 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 ILPs 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.

Full work available at URL: https://arxiv.org/abs/1308.2858

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