Approximating the bundled crossing number
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 polynomial-time algorithm to compute an
8-approximation 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 8-approximation.
In the special case of circular drawings the approximation factor is 8, this improves
upon the 10-approximation of Fink et al. [14]. 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 9/2-approximation when the intersection graph of
the pseudosegments is bipartite and has no toothed hole.
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6
433-457
433-457
Brown University
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