On Minimum k-Modal Partitions of Permutations

  title={On Minimum k-Modal Partitions of Permutations},
  author={Gabriele Di Stefano and Stefan Krause and Marco E. L{\"u}bbecke and Uwe T. Zimmermann},
Partitioning a permutation into a minimum number of monotone subsequences is NP-hard. We extend this complexity result to minimum partitioning into k-modal subsequences, that is, subsequences having at most k internal extrema. Based on a network flow interpretation we formulate both, the monotone and the k-modal version, as mixed integer programs. This is the first proposal to obtain provably optimal partitions of permutations. From these models we derive an LP rounding algorithm which is a 2… CONTINUE READING