Intersection Problems on Segments Under Boundary Updates With Application to Persistent Lists

Abstract

We consider some intersection problems on segments of H 2 in the partially dynamic setting called boundary update, where updates occur at the boundary of a given region. In particular, we maintain a set S of line segments under (boundary) insertions and deletions, such that, given a line segment t either of fixed slope or originating from a fixed point and given a point p € S D £, we can efficiently and orderly report all segments intersecting £; insertions/deletions of segments occur at the boundaries of a vertical infinite slab. We provide practical algorithms requiring C?(|<S|) space, C?(log|«S|) time per update and OQ\) time per query, where k is the number of reported segments. Our results allow both modeling a moving window over a larger data set and answering segment intersection queries at an extra query cost of 0(log|«S|); also, they provide a methodology for designing access methods to temporal databases as well as a new kind of partially persistent lists.