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A simple digraph is semi-complete if for any two of its vertices u and v, at least one of the arcs (u,v) and (v,u) is present. We study the complexity of computing two layout parameters of semi-complete digraphs: cutwidth and optimal linear arrangement (OLA). We prove that: (1) Both parameters are NP-hard to compute and the known exact and parameterized algorithms for them have essentially optimal running times, assuming the Exponential Time Hypothesis; (2) The cutwidth parameter admits aarXiv:1706.00617v1 fatcat:7aoy6ah4znbbzc6u77xckl2hwe