文章基本信息

标题：Untangling Circular Drawings: Algorithms and Complexity
本地全文：下载
作者：Bhore, Sujoy ; Li, Guangping ; Nöllenburg, Martin 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：212
DOI：10.4230/LIPIcs.ISAAC.2021.19
语种：English
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We consider the problem of untangling a given (non-planar) straight-line circular drawing δ_G 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°(δ_G) as the minimum number of vertices that need to be shifted to resolve all crossings of δ_G. We show that the problem Circular Untangling, asking whether shift°(δ_G) ≤ 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°(δ_G) ≤ ⌊n/2⌋-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.
关键词：graph drawing;straight-line drawing;outerplanarity;NP-hardness;untangling