This paper concerns the problem of sweeping a pseudoline arrangement with n x-monotone curves with a rope (an x-monotone curve that connects the points of infinity). The only movement permitted for the rope is to flip parts of it from the lower to the upper chain of the face defined by the arrangement. Counting as length of the rope the number of edges, what rope-length can be needed in such a sweep? We show that all such arrangements can be swept with rope-length at most 2n−2, and for some arrangements rope-length at least 7n/4- O(1) is required. We also discuss some complexity issues around the problem of computing a sweep with the shortest rope-length.
Last update: July 3, 2025.