par Akitaya, Hugo Alves;Biniaz, Ahmad;De Carufel, Jean Lou;Iacono, John 
;Smid, Michiel M.;Theocharous, Leonidas;Aloupis, Greg ;Bose, Prosenjit ;Gavoille, Cyril;Kleist, Linda;Souvaine, Diane D.L.
Référence Leibniz international proceedings in informatics, 351, 75
Publication Publié, 2025-10-01
;Smid, Michiel M.;Theocharous, Leonidas;Aloupis, Greg ;Bose, Prosenjit ;Gavoille, Cyril;Kleist, Linda;Souvaine, Diane D.L.Référence Leibniz international proceedings in informatics, 351, 75
Publication Publié, 2025-10-01
Article révisé par les pairs
| Résumé : | A covering path for a finite set P of points in the plane is a polygonal path such that every point of P lies on a segment of the path. The vertices of the path need not be at points of P. A covering path is plane if its segments do not cross each other. Let π(n) be the minimum number such that every set of n points in the plane admits a plane covering path with at most π(n) segments. We prove that π(n) ≤ ⌈6n/7⌉. This improves the previous best-known upper bound of ⌈21n/22⌉, due to Biniaz (SoCG 2023). Our proof is constructive and yields a simple O(nlog n)-time algorithm for computing a plane covering path. |
