Lecture 22 — April 29

Up until now, we have mainly studied how to decrease the query time, and the preprocessing time of our data structures. In this lecture, we will focus on maintaining the data as compactly as possible. Our goal will be to get as close the information theoretic optimum as possible. We will refer to this optimum as OPT. Note that most ”linear space” data structures we have seen are still far from the information theoretic optimum because they typically use O(n) words of space, whereas OPT usually uses O(n) bits. This strict space limitation makes it really hard to have dynamic data structures, so most space-efficient data structures are static.