Efficient Computation of Representative Families with Applications in Parameterized and Exact Algorithms

@article{Fomin2016EfficientCO,
  title={Efficient Computation of Representative Families with Applications in Parameterized and Exact Algorithms},
  author={Fedor V. Fomin and Daniel Lokshtanov and Fahad Panolan and Saket Saurabh},
  journal={J. ACM},
  year={2016},
  volume={63},
  pages={29:1-29:60}
}
Let <i>M</i>=(<i>E</i>, <i>I</i>) be a matroid and let <i>S</i>={<i>S</i><sub>1</sub>, ċ , <i>S</i><sub>t</sub>} be a family of subsets of <i>E</i> of size <i>p</i>. A subfamily <i>Ŝ</i> ⊆ <i>S</i> is <i>q</i>-<i>representative</i> for <i>S</i> if for every set <i>Y</i>⊆<i>E</i> of size at most <i>q</i>, if there is a set <i>X</i> ∈ <i>S</i> disjoint from <i>Y</i> with <i>X</i>∪ <i>Y</i> ∈ <i>I</i>, then there is a set <i>&Xcirc;</i> ∈ <i>Ŝ</i> disjoint from <i>Y</i> with <i>&Xcirc;</i> ∪ <i>Y… CONTINUE READING
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