Few crossings
A preprint of my SODA paper with Mike Goodrich and Darren Strash, “Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Crossings,” is now up on arxiv. There's a bit of a connection with my ACM GIS paper with Mike on road networks: the GIS paper included data suggesting that real-world road networks have few crossings, so both papers provide fast algorithms for these networks. But the GIS paper based the algorithms on a different assumption, involving representing the network as a low-ply disk system, while the SODA paper uses only the crossing number and the connectivity of the graph.