## Information

- Publication Type: Conference Paper
- Workgroup(s)/Project(s):
- Date: December 2021
- Publisher: LIPICS
- Pages (to): 17
- Pages (from): 1
- Lecturer: Guangping Li
- Event: The 32nd International Symposium on Algorithms and Computation
- DOI: 10.4230/LIPIcs.ISAAC.2021.19
- Call for Papers: Call for Paper
- Booktitle: Proceedings of the 32nd International Symposium on Algorithms and Computation
- Pages: 17

## 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.## Additional Files and Images

## Weblinks

- Entry in reposiTUm (TU Wien Publication Database)
- Entry in the publication database of TU-Wien
- DOI: 10.4230/LIPIcs.ISAAC.2021.19

## BibTeX

@inproceedings{bhore-2021-issac, title = "Untangling Circular Drawings: Algorithms and Complexity", author = "Sujoy Bhore and Guangping Li and Martin N\"{o}llenburg and Ignaz Rutter and Hsiang-Yun Wu", year = "2021", 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.", month = dec, publisher = "LIPICS", event = "The 32nd International Symposium on Algorithms and Computation", doi = "10.4230/LIPIcs.ISAAC.2021.19", booktitle = "Proceedings of the 32nd International Symposium on Algorithms and Computation", pages = "17", pages = "1--17", URL = "https://www.cg.tuwien.ac.at/research/publications/2021/bhore-2021-issac/", }