Finding Branch-Decompositions and Rank-Decompositions

  title={Finding Branch-Decompositions and Rank-Decompositions},
  author={Petr Hlinen{\'y} and Sang-il Oum},
  journal={SIAM J. Comput.},
We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most k if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parameter tractable, that is, they run in time O(n3) for each fixed value of k where n is the number of vertices / elements of the input… CONTINUE READING

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