Approximating the bundled crossing number

Arroyo Guevara AM, Felsner S. 2022. Approximating the bundled crossing number. WALCOM 2022: Algorithms and Computation. WALCOM: Algorithms and ComputationLNCS vol. 13174, 383–395.


Conference Paper | Published | English

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Author
Arroyo Guevara, Alan MISTA ; Felsner, Stefan
Department
Abstract
Bundling crossings is a strategy which can enhance the readability of graph drawings. In this paper we consider bundlings for families of pseudosegments, i.e., simple curves such that any two have share at most one point at which they cross. Our main result is that there is a polynomial-time algorithm to compute an 8-approximation of the bundled crossing number of such instances (up to adding a term depending on the facial structure). This 8-approximation also holds for bundlings of good drawings of graphs. In the special case of circular drawings the approximation factor is 8 (no extra term), this improves upon the 10-approximation of Fink et al. [6]. We also show how to compute a 92-approximation when the intersection graph of the pseudosegments is bipartite.
Publishing Year
Date Published
2022-03-16
Proceedings Title
WALCOM 2022: Algorithms and Computation
Acknowledgement
This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1.
Volume
13174
Page
383-395
Conference
WALCOM: Algorithms and Computation
Conference Location
Jember, Indonesia
Conference Date
2022-03-24 – 2022-03-26
ISSN
eISSN
IST-REx-ID

Cite this

Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. In: WALCOM 2022: Algorithms and Computation. Vol 13174. LNCS. Springer Nature; 2022:383-395. doi:10.1007/978-3-030-96731-4_31
Arroyo Guevara, A. M., & Felsner, S. (2022). Approximating the bundled crossing number. In WALCOM 2022: Algorithms and Computation (Vol. 13174, pp. 383–395). Jember, Indonesia: Springer Nature. https://doi.org/10.1007/978-3-030-96731-4_31
Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” In WALCOM 2022: Algorithms and Computation, 13174:383–95. LNCS. Springer Nature, 2022. https://doi.org/10.1007/978-3-030-96731-4_31.
A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” in WALCOM 2022: Algorithms and Computation, Jember, Indonesia, 2022, vol. 13174, pp. 383–395.
Arroyo Guevara AM, Felsner S. 2022. Approximating the bundled crossing number. WALCOM 2022: Algorithms and Computation. WALCOM: Algorithms and ComputationLNCS vol. 13174, 383–395.
Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” WALCOM 2022: Algorithms and Computation, vol. 13174, Springer Nature, 2022, pp. 383–95, doi:10.1007/978-3-030-96731-4_31.
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