6.838, Computational Geometry; Fall 2001

Point Location

Sergi Elizalde & David Pritchard

Naïve Algorithm - Analysis

Total running time is O(log n):

O(log n) - binary search against O(n) vertices of S

O(log n) - binary search against up to n segments intersecting the slab

What about storage space? For each slab, we need to keep an array long enough to hold all of the segments intersecting the slab.

Storage space required can be as bad as O(n²):

Although it may not be quadratic in practice, textbook suggests typical storage required would be O(n^3/2)