Learning objectives

After this class, you should be able to:

1. Describe how a d-dimensional range tree can be constructed, derive the time and space complexity for constructing it, and derive the time complexity for querying it.
2. Give a set of points, show how they can be transformed to composite points, construct a range tree based on the composite points, and show how it can be queried.
3. Given a set of points, construct a layered range tree, and show the steps involved in querying it.
4. Derive the space and time complexity for constructing a 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. Prove, using induction, the time complexity given in CG for constructing a d-dimensional range tree.
  2. Consider the node on the right side at the second level of figure 5.9 in CG. Show the array corresponding to its children, and all pointers to the children.

• 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.