Shortcuts: For common scenarios, we pre-calculate the travel time/distance (the "shortcut") between border points within the same cluster and also to border points of immediately adjacent clusters.
For our proof we develop techniques for flip sequences of triangulations whose counterparts were introduced for the study of flip sequences of non-crossing spanning trees by Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber~[SODA25] and Bjerkevik, Dorfer, Kleist, Ueckerdt, and Vogtenhuber~[SoCG26].，详情可参考下载安装汽水音乐
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