d abstract) Lars Arge1 , Darren Erik Vengroff2 , and Jeffrey Scott Vitter3 1 BRICS† , Department of Computer Science, University of Aarhus, Aarhus, Denmark 2 Department of Computer Science, Brown University, Providence, RI 02912, USA 3 Department of Computer Science, Duke University, Durham, NC 27708, USA In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient new external-memory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red-blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems, the first three problems are useful for rendering and modeling, and the latter two...