Lecture 20

Learning objectives

After this class, you should be able to:

1. Given a set of points, construct a layered range tree, and show the steps involved in querying it.
2. Derive the space and time complexity for constructing a layered range tree, and for querying it.

Reading assignment

1. Handout on Orthogonal range searching.
2. CLR: Page 906 and 907.

Exercises and review questions

• Questions on current lecture's material
  1. 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 layered 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.
  2. Prove the time complexity given in CG for constructing a d-dimensional layered range tree.

• Questions on next lecture's material
  1. Given the text abcdabcdab, and the pattern abcdab, give all valid shifts, and an example of an invalid shift.
  2. (Post your answer on the discussion board) Give an application of string matching.