In the next two lectures we study the question of dynamic optimality, or whether there exists a binary search tree algorithm that performs ”as well” as all other algorithms on any input string. In this lecture we will define a binary search tree as a formal model of computation, show some analytic bounds that a dynamically optimal binary search tree needs to satisfy, and show two search trees t...

In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence—any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any othe...

In the next two lectures we study the question of dynamic optimality, or whether there exists a binary search tree algorithm that performs ”as well” as all other algorithms on any input string. In this lecture we will define a binary search tree as a formal model of computation, show some analytic bounds that a dynamically optimal binary search tree needs to satisfy, and show two search trees t...

Binary search trees are a fundamental data structure. There are two complexity metrics commonly associated with them: the maximum number of comparisons made during a search and the expected number of comparisons made during a search. Minimizing these metrics, separately or together, has been extensively studied. The difficulty of doing this depends on how much information is given. There are 2n...

In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been recently extended by [Emamjomeh-Zadeh et al., STOC, 2016] to the problem of detecting a target in an arbitrary graph. Similarly to the classical case in the path, the algorithm of Emamjom...

In a randomly grown binary search tree (BST) of size n, any xed pattern occurs with a frequency that is on average proportional to n. Deviations from the average case are highly unlikely and well quantiied by a Gaussian law. Trees with forbidden patterns occur with an exponentially small probability that is characterized in terms of Bessel functions. The results obtained extend to BSTs a type o...

Although IP address lookup schemes using ternary content addressable memory (TCAM) can perform high speed packet forwarding, TCAM is much more expensive than ordinary memory in implementation cost. As a low-cost solution, binary search algorithms such as a binary trie or a binary search tree have been widely studied. This paper proposes an efficient IP address lookup scheme using balanced binar...

Since the origins of the constraint satisfaction paradigm, its restriction to binary constraints has concentrated a signiicant part of the work. This is understandable because new ideas/techniques are usually much simpler to present/ elaborate by rst restricting them to the binary case. (See for example the arc consistency algorithms, such as AC-3 or AC-4, which have been presented rst in their...

The presence of geometric details on object surfaces dramatically changes the way light interacts with these surfaces. Although synthesizing realistic pictures requires simulating this interaction as faithfully as possible, explicitly modeling all the small details tends to be impractical. To address these issues, an image-based technique called relief mapping has recently been introduced for a...