Orthogonal queries in segments

Abstract

We consider theorthgonal clipping problem in a set of segments: Given a set ofn segments ind-dimensional space, we preprocess them into a data structure such that given an orthogonal query window, the segments intersecting it can be counted/reported efficiently. We show that the efficiency of the data structure significantly depends on a geometric discrete parameterK named theProjected-image complexity, which becomes ź(n2) in the worst case but practically much smaller. If we useO(m) space, whereK log4dź7nźmźn log4dź7n, the query time isO((K/m)1/2 logmax{4, 4dź5}n). This is near to an Ω((K/m)1/2) lower bound.