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Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width

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arxiv 1509.03753 v2 pith:JVYQWF4R submitted 2015-09-12 cs.DS

Petr A. Golovach , Pinar Heggernes , Mamadou Moustapha Kanté , Dieter Kratsch , Sigve H. S{ae}ther , Yngve Villanger This is my paper · ORCID
classification cs.DS
keywords boundedgraphslmim-widthdominatinglinearminimalpolynomialsets
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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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