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Open Courseware

Dynamic Optimality: Binary Search Trees, Analytic Bounds, Splay Trees, Geometric View, Greedy Algorithm

Have you ever wondered how to represent a binary search tree on n nodes as a set of n points in 2D? Today’s lecture will reveal a surprising new (2009) such connection, which provides an approach to tackling the venerable dynamic optimality conjecture.The dynamic optimality conjecture is one of the oldest and biggest open problems […]

Open Courseware

Greedy Algorithms (and Graphs)

Open Courseware

Greedy Algorithms, Software Design and Debugging

Open Courseware

Dynamic Optimality: Independent Rectangle, Wilber, And Signed Greedy Lower Bounds; Key-Independent Optimality; O(Lg Lg N)-Competitive Tango Trees

In this lecture, we’ll see the best binary search tree we know, in the sense of achieving the best known competitive ratio of O(lg lg n) compared to the offline optimal. To analyze these “Tango trees”, we compare against a lower bound. Specifically, we describe a Signed Greedy algorithm that, for a given access sequence, computes a number […]