Work Note 11, DM819, fall 2009

Discussion Section December 1

• Exercises 10.2, 10.5, 10.6(a), 10.9, 10.10.

  Exercises 10.2 and 10.5 are the hardest. So, also consider the other problems even if these cause you some difficulties. In 10.2, you do not need to build a priority search tree which looks exactly like the structure build using the normal construction method. You should just build something with the same asymptotic properties.

• Preprocess a set S of n intervals so that the following type of queries can be answered efficiently. A query consists of an interval q_I = [q_x:q_y] and an element q_e∈q_I. One must report all intervals from S that are contained in q_I and contain q_e.

  Origin of the problem (not relevant for solving it): The problem comes from query optimization in streaming databases. Streams are at the leaves of the evaluation tree and predicates may compare elements in different streams. Predicates must be evaluated at a node where all information is available (the "contained in" requirement). Among the possible nodes, it is most efficient to evaluate it as far down in the tree as possible. If it does not involve streams on both sides of the root of the subtree (q_e), then it can be pushed further down (the "contains" requirement).

Lecture December 4

• Quadtrees (chapter 14).