INTERSECTION PROBLEMS ON SEGMENTS UNDER BOUNDARY UPDATES WITH APPLICATION TO PERSISTENT LISTS

Abstract

We consider some intersection problems on segments of [Formula: see text] 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 ℓ either of fixed slope or originating from a fixed point and given a point p∈S∩ℓ, we can efficiently and orderly report all segments intersecting ℓ; insertions/deletions of segments occur at the boundaries of a vertical infinite slab. We provide practical algorithms requiring [Formula: see text] space, [Formula: see text] time per update and [Formula: see text] 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 [Formula: see text]; also, they provide a methodology for designing access methods to temporal databases as well as a new kind of partially persistent lists.