@inproceedings{c4c6b8e1a65e47809aa39b8fc7aa5999,

title = "Untangling Circular Drawings: Algorithms and Complexity",

abstract = "We consider the problem of untangling a given (non-planar) straight-line circular drawing δG of an outerplanar graph G = (V, E) into a planar straight-line circular drawing by shifting a minimum number of vertices to a new position on the circle. For an outerplanar graph G, it is clear that such a crossing-free circular drawing always exists and we define the circular shifting number shift◦(δG) as the minimum number of vertices that need to be shifted to resolve all crossings of δG. We show that the problem Circular Untangling, asking whether shift◦(δG) ≤ K for a given integer K, is NP-complete. Based on this result we study Circular Untangling for almost-planar circular drawings, in which a single edge is involved in all the crossings. In this case we provide a tight upper bound shift◦(δG) ≤ ⌊n2 ⌋ - 1, where n is the number of vertices in G, and present a polynomial-time algorithm to compute the circular shifting number of almost-planar drawings.",

keywords = "Graph drawing, NP-hardness, Outerplanarity, Straight-line drawing, Untangling",

author = "Sujoy Bhore and Guangping Li and Martin N{\"o}llenburg and Ignaz Rutter and Wu, {Hsiang Yun}",

note = "Publisher Copyright: {\textcopyright} Sujoy Bhore, Guangping Li, Martin N{\"o}llenburg, Ignaz Rutter, and Hsiang-Yun Wu.; 32nd International Symposium on Algorithms and Computation, ISAAC 2021 ; Conference date: 06-12-2021 Through 08-12-2021",

year = "2021",

month = dec,

day = "1",

doi = "10.4230/LIPIcs.ISAAC.2021.19",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Hee-Kap Ahn and Kunihiko Sadakane",

booktitle = "32nd International Symposium on Algorithms and Computation, ISAAC 2021",

address = "Germany",

}