Lecture 18

Learning objectives

After this class, you should be able to:

1. Given a set of points in 1 or 2 dimensions, construct a range tree for it, and show each step in the range search algorithm to answer an orthogonal range query using the algorithms discussed in class.
2. Prove the time and space complexities of the algorithms discussed in class, for orthogonal range search.

Reading assignment

1. Handout on Orthogonal range searching, Introduction, sections 5.1 and 5.3.

Exercises and review questions

• Questions on current lecture's material
  1. Write an algorithm for searching the right subtree of the split node in a 1-dimensional range search.
  2. Show how a 2-dimensional range tree can be constructed in O(n log n) time. You can use the data for the next question and demonstrate your technique.
  3. Given the following points: P = {(1.1,1.1), (2.1,1.2), (3.1,1.3), (1.2,2.1), (2.2,2.2), (3.2,2.3), (1.3,3.1), (2.3,3.2), (3.3,3.3)}, construct a 2-d range tree and show the steps in retrieving points in the following region: x = 1.2, x' = 3.15, y = 1.3, y' = 3.3.

• Questions on next lecture's material
  1. None.