Inserting Multiple Edges into a Planar Graph
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Proceedings |
| Conference | 32nd International Symposium on Computational Geometry (SoCG 2016) |
| MU Faculty or unit | |
| Citation | |
| Web | http://socg2016.cs.tufts.edu/ |
| Doi | http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.30 |
| Field | Informatics |
| Keywords | crossing number; crossing minimization; planar insertion |
| Description | Let G be a connected planar (but not yet embedded) graph and F a set of additional edges not in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. An optimal solution to this problem is known to approximate the crossing number of the graph G+F. Finding an exact solution to MEI is NP-hard for general F, but linear time solvable for the special case of |F|=1 [Gutwenger et al, SODA 2001/Algorithmica] and polynomial time solvable when all of F are incident to a new vertex [Chimani et al, SODA 2009]. The complexity for general F but with constant k=|F| was open, but algorithms both with relative and absolute approximation guarantees have been presented [Chuzhoy et al, SODA 2011], [Chimani-Hlineny, ICALP 2011]. We show that the problem is fixed parameter tractable (FPT) in k for biconnected G, or if the cut vertices of G have bounded degrees. We give the first exact algorithm for this problem; it requires only O(|V(G)|) time for any constant k. |
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