Abstract
The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on graphs of bounded LMIM-width and graphs of bounded local LMIM-width. In particular, we show that all 1-minimal and all 1-maximal \((\sigma ,\rho )\)-dominating sets, and hence all minimal dominating sets, of graphs of bounded LMIM-width can be enumerated with polynomial (linear) delay using polynomial space. Furthermore, we show that all minimal dominating sets of a unit square graph can be enumerated in incremental polynomial time.
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Notes
The original statement dealt with un-colored graphs, however it is not hard to extend it to colored graphs.
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A preliminary version of this paper appeared as an extended abstract in the proceedings of ISAAC 2015. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 267959. M.M. Kanté and D. Kratsch are supported by French Agency for Research under the GraphEn Project (ANR-15-CE-0009).
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Golovach, P.A., Heggernes, P., Kanté, M.M. et al. Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width. Algorithmica 80, 714–741 (2018). https://doi.org/10.1007/s00453-017-0289-1
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DOI: https://doi.org/10.1007/s00453-017-0289-1