Area requirement of graph drawings with few crossings per edge

In this paper we study how to compute compact straight-line drawings of planar graphs with a limited number of crossings per edge. We prove that every outerplanar graph can be drawn in O(n log n) area using a sub-linear number of crossings per edge, and that for any given number ε>0, every outerplanar graph admits an O(n^(1+ε)) area drawing with O(n^(1−ε)) crossing per edge. The drawing algorithms run in linear time and can be also generalized to another meaningful sub-family of series–parallel graphs with bounded vertex-degree.