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arXiv · 1509.03753

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

Petr A. Golovach·Pinar Heggernes·Mamadou Moustapha Kanté·Dieter Kratsch·Sigve H. Sæther·Yngve Villanger
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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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Petr A. Golovach, Pinar Heggernes, Mamadou Moustapha Kanté, Dieter Kratsch, Sigve H. Sæther, Yngve Villanger. 2015-09-12. Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width. https://arxiv.org/abs/1509.03753

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