(Wireless) Scheduling, Graph Classes, and c-Colorable Subgraphs.
Matthias Bentert, René van Bevern, Rolf Niedermeier · arXiv (Cornell University) · 2017
Inductive inductive $k$-independent graphs are a generalization of 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 $c$-colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting $c$ sets of pairwise non-conflicting jobs (modeled as graph vertices). We investigate the parameterized complexity of this problem on inductive inductive $k$-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. On the contrary, we prove that the more general Maximum $c$-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 inductive 1-independent and inductive inductive 2-independent graphs with applications in scheduling.