A Topological Algorithm for Determining How Road Networks Evolve Over   Time
  We provide an efficient algorithm for determining how a road network has evolved over time, given two snapshot instances from different dates. To allow for such determinations across different databases and even against hand drawn maps, we take a strictly topological approach in this paper, so that we compare road networks based strictly on graph-theoretic properties. Given two road networks of same region from two different dates, our approach allows one to match road network portions that remain intact and also point out added or removed portions. We analyze our algorithm both theoretically, showing that it runs in polynomial time for non-degenerate road networks even though a related problem is NP-complete, and experimentally, using dated road networks from the TIGER/Line archive of the U.S. Census Bureau. 
M T Goodrich, Siddharth Gupta, Manuel R. Torres
cs.DS cs.CG