If a connected graph corresponds to a set of points and line segments in the plane, in such a way that the number of crossing pairs of line segments is sublinear in the size of the graph by an iterated-log factor, then we can find the arrangement of the segments in linear time. It was previously known how to find the arrangement in linear time when the number of crossings is superlinear by an iterated-log factor, so the only remaining open case is when the number of crossings is close to the size of the graph.
Co-authors -- Publications -- David Eppstein -- Theory Group -- Inf. & Comp. Sci. -- UC Irvine
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