Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width
Data Structures and Algorithms
2015-09-16 v2
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.
Cite
@article{arxiv.1509.03753,
title = {Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width},
author = {Petr A. Golovach and Pinar Heggernes and Mamadou Moustapha Kanté and Dieter Kratsch and Sigve H. Sæther and Yngve Villanger},
journal= {arXiv preprint arXiv:1509.03753},
year = {2015}
}