Flipping Plane Spanning Paths

Aichholzer, Oswin; Knorr, Kristin; Mulzer, Wolfgang; Obenaus, Johannes; Paul, Rosna; Vogtenhuber, Birgit

doi:10.1007/978-3-031-27051-2_5

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Cited by 2 publications

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“…They have also been considered for non-crossing trees [1] and paths. It is possible to reconfigure any two noncrossing paths if the points are in convex position [4,11] or if there is one point inside the convex hull [2].…”

Section: Related Reconfiguration Problemsmentioning

confidence: 99%

On the Longest Flip Sequence to Untangle Segments in the Plane

Fonseca

Gerard

Bastien

2023

Lecture Notes in Computer Science

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A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and insert a pair of non-crossing segments, while keeping the same vertex degrees. The goal of this paper is to devise efficient strategies to flip the segments in order to obtain crossing-free segments after a small number of flips. Linear and near-linear bounds on the number of flips were only known for segments with endpoints in convex position. We generalize these results, proving linear and near-linear bounds for cases with endpoints that are not in convex position. Our results are proved in a general setting that applies to multiple problems, using multigraphs and the distinction between removal and insertion choices when performing a flip.

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Section: Related Reconfiguration Problemsmentioning

confidence: 99%