Inductive $k$-independent graphs and $c$-colorable subgraphs in scheduling: A review
Abstract
Inductive -independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced -colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting sets of pairwise non-conflicting jobs (modeled as graph vertices). We investigate the parameterized complexity of this problem on inductive -independent graphs. We show that the Independent Set problem is W[1]-hard even on 2-simplicial 3-minoes---a subclass of inductive 2-independent graphs. In contrast, we prove that the more general Maximum -Colorable Subgraph problem is fixed-parameter tractable on edge-wise unions of cluster and chordal graphs, which are 2-simplicial. In both cases, the parameter is the solution size. Aside from this, we survey other graph classes between inductive 1-inductive and inductive 2-inductive graphs with applications in scheduling.
Keywords
Cite
@article{arxiv.1712.06481,
title = {Inductive $k$-independent graphs and $c$-colorable subgraphs in scheduling: A review},
author = {Matthias Bentert and René van Bevern and Rolf Niedermeier},
journal= {arXiv preprint arXiv:1712.06481},
year = {2019}
}