A note on computing set overlap classes

@article{Charbit2008ANO,
  title={A note on computing set overlap classes},
  author={P. Charbit and M. Habib and V. Limouzy and F. D. Montgolfier and M. Raffinot and M. Rao},
  journal={Inf. Process. Lett.},
  year={2008},
  volume={108},
  pages={186-191}
}
Let V be a finite set of n elements and F={X"1,X"2,...,X"m} a family of m subsets of V. Two sets X"i and X"j of F overlap if X"i@?X"j @A, X"j@?X"i @A, and X"i@?X"j @A. Two sets X,Y@?F are in the same overlap class if there is a series X=X"1,X"2,...,X"k=Y of sets of F in which each X"iX"i"+"1 overlaps. In this note, we focus on efficiently identifying all overlap classes in O(n+@?"i"="1^m|X"i|) time. We thus revisit the clever algorithm of Dahlhaus [E. Dahlhaus, Parallel algorithms for… Expand
Consecutive Ones Property Testing: Cut or Swap
Computing galled networks from real data
Linear Time Split Decomposition Revisited
Efficient Algorithms for Finding Tucker Patterns
Split decomposition and graph-labelled trees: characterizations and fully-dynamic algorithms for totally decomposable graphs
Methods for Phylogenetic Reconstruction
...
1
2
...

References

SHOWING 1-5 OF 5 REFERENCES
A certifying algorithm for the consecutive-ones property
Set overlap classes computation, source code
  • Set overlap classes computation, source code
  • 2007
An example (continued) of the resulting subgraph is shown in Figure 5
  • An example (continued) of the resulting subgraph is shown in Figure 5