Fixed parameter tractability of crossing minimization of almost-trees
Michael J. Bannister, David Eppstein, Joseph A. Simons
TL;DR
This paper studies the problem of minimizing crossings in graphs close to trees, providing fixed parameter tractable algorithms for various crossing minimization variants in nearly-tree graphs.
Contribution
It introduces fixed parameter tractable algorithms for crossing minimization problems on graphs that are close to trees, such as 1-page and 2-page book crossing numbers.
Findings
Fixed parameter tractable algorithms for 1-page and 2-page crossing numbers.
Efficient algorithms for crossing minimization in graphs with few extra edges.
Applicable to graphs differing from trees by a small number of edges.
Abstract
We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms for the 1-page book crossing number, the 2-page book crossing number, and the minimum number of crossed edges in 1-page and 2-page book drawings.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Optimization and Packing Problems