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Special Issue on Parameterized and Approximation Algorithms in Graph Drawing
DOI: 10.7155/jgaa.00629
Approximating the Bundled Crossing Number
Alan Arroyo and
Stefan Felsner
Vol. 27, no. 6, pp. 433457, 2023. Regular paper.
Abstract Bundling crossings is a strategy which can enhance the readability of graph
drawings. In this paper we consider good drawings, i.e., we require that
any two edges have at most one common point which can be a common vertex or
a crossing. Our main result is that there is a polynomialtime algorithm to
compute an 8approximation of the bundled crossing number of a good drawing
with no toothed hole. In general the number of toothed holes has to
be added to the 8approximation. In the special case of circular drawings
the approximation factor is 8, this improves upon the
10approximation of Fink et al.[Fink et al., LATIN 2016]. Our approach also works with
the same approximation factor for families of pseudosegments, i.e., curves
intersecting at most once. We also show how to compute a
$\frac{9}{2}$approximation when the intersection graph of the
pseudosegments is bipartite and has no toothed hole.
This work is licensed under the terms of the CCBY license.

Submitted: May 2022.
Reviewed: October 2022.
Revised: November 2022.
Accepted: April 2023.
Final: April 2023.
Published: July 2023.

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