### Abstract

The np-hard independent set problem is to determine for a given graph g and an integer k whether g contains a set of k pairwise non-adjacent vertices. The problem has numerous applications in scheduling, including resource allocation and steel manufacturing. There, one encounters restricted graph classes such as 2-union graphs, which are edge-wise unions of two interval graphs on the same vertex set, or strip graphs, where additionally one of the two interval graphs is a disjoint union of cliques.we prove np-hardness of independent set on a very restricted subclass of 2-union graphs and identify natural parameterizations to chart the possibilities and limitations of effective polynomial-time preprocessing (kernelization) and fixed-parameter algorithms. Our algorithms benefit from novel formulations of the computational problems in terms of (list-)colored interval graphs.

Original language | English |
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Title of host publication | Algorithms and Computation |

Subtitle of host publication | 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 2012 Proceedings |

Editors | Kun-Mao Chao, Tsan-sheng Hsu, Der-Tsai Lee |

Publisher | Springer |

Pages | 247-256 |

Volume | 7676 |

ISBN (Electronic) | 978-3-642-35261-4 |

ISBN (Print) | 978-3-642-35260-7 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 7676 |

## Cite this

van Bevern, R., Mnich, M., Niedermeier, R., & Weller, M. (2012). Interval Scheduling and Colorful Independent Sets. In K-M. Chao, T. Hsu, & D-T. Lee (Eds.),

*Algorithms and Computation: 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 2012 Proceedings*(Vol. 7676, pp. 247-256). Springer. Lecture Notes in Computer Science, Vol.. 7676 https://doi.org/10.1007/978-3-642-35261-4_28