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An Improved Bound for Plane Covering Paths

par Akitaya, Hugo Alves;Aloupis, Greg ;Biniaz, Ahmad;Bose, Prosenjit ;De Carufel, Jean Lou;Gavoille, Cyril;Iacono, John ;Kleist, Linda;Smid, Michiel M.;Souvaine, Diane D.L.;Theocharous, Leonidas
Référence arXiv.org, arXiv:2507.06477
Publication Publié, 2025-07-08

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Résumé :

A covering path for a finite set of points in the plane is a polygonal path such that every point of lies on a segment of the path. The vertices of the path need not be at points of . A covering path is plane if its segments do not cross each other. Let be the minimum number such that every set of points in the plane admits a plane covering path with at most segments. We prove that . This improves the previous best-known upper bound of , due to Biniaz (SoCG 2023). Our proof is constructive and yields a simple -time algorithm for computing a plane covering path