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Partitioning a permutation into a minimum number of monotone subsequences is N P-hard. We extend this complexity result to minimum partitioning into k-modal subsequences; here unimodal is the special case k = 1. 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. LP rounding gives a 2-approximation for minimum monotone partitions and a (k +doi:10.1016/j.jda.2008.01.002 fatcat:xpik3ui5znfxbcux2tje2pmd3m