2026-07-22T13:00:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7208 2024-03-06T10:40:00Z ddc:004 open_access

On Bend-Minimized Orthogonal Drawings of Planar 3-Graphs Chang, Yi-Jun Yen, Hsu-Chun Bend minimization graph drawing orthogonal drawing planar graph An orthogonal drawing of a graph is a planar drawing where each edge is drawn as a sequence of horizontal and vertical line segments. Finding a bend-minimized orthogonal drawing of a planar graph of maximum degree 4 is NP-hard. The problem becomes tractable for planar graphs of maximum degree 3, and the fastest known algorithm takes O(n^5 log n) time. Whether a faster algorithm exists has been a long-standing open problem in graph drawing. In this paper we present an algorithm that takes only O~(n^{17/7}) time, which is a significant improvement over the previous state of the art. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yi-Jun Chang and Hsu-Chun Yen 2017 Is Part Of LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2017.29 urn:nbn:de:0030-drops-72080 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.29 eng https://creativecommons.org/licenses/by/3.0/legalcode