Parameterized Algorithms for Modular-Width
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Proceedings |
| Conference | Parameterized and Exact Computation |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-319-03898-8_15 |
| Field | Informatics |
| Keywords | parameterized complexity; modular width; shrub depth; chromatic number; hamiltonian path |
| Description | 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. |
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