Inductive $$k$$ k -independent graphs and c-colorable subgraphs in scheduling: a review

Matthias Bentert (), René Bevern () and Rolf Niedermeier ()
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Matthias Bentert: Algorithmics and Computational Complexity, Faculty IV
René Bevern: Novosibirsk State University
Rolf Niedermeier: Algorithmics and Computational Complexity, Faculty IV

Journal of Scheduling, 2019, vol. 22, issue 1, No 2, 3-20

Abstract: Abstract Inductive $$k$$ k -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 c-colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting $$c$$ c sets of pairwise non-conflicting jobs (modeled as graph vertices). We investigate the parameterized complexity of this problem on inductive $$k$$ k -independent graphs. We show that the Maximum 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 Max-Weightc-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 $$1$$ 1 -independent and inductive $$2$$ 2 -independent graphs with applications in scheduling.

Keywords: Independent set; Job interval selection; Interval graphs; Chordal graphs; Inductive $$k$$ k -independent graphs; NP-hard problems; Parameterized complexity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10951-018-0595-8

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