Every arrangement of n x-monotone pseudolines admits a sweep with rope length at most 2n-2, and some arrangements require at least 7(n-2)/4+1.
A simple aggregative algorithm for counting triangu- lations of planar point sets and related problems
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Sweeping $x$-monotone pseudolines
Every arrangement of n x-monotone pseudolines admits a sweep with rope length at most 2n-2, and some arrangements require at least 7(n-2)/4+1.