We study the number of records in a random binary search tree on n randomly labelled vertices. Equivalently the number of random cuttings required to eliminate a random binary search tree can be studied. After normalization the distribution is shown to be asymptotically 1-stable.

In this paper, we present a system capable of dynamically learning shapes in a way that also allows for the dynamic deletion of shapes already learned. It uses a self-balancing Binary Search Tree (BST) data structure in which we can insert shapes that we can later retrieve and also delete inserted shapes. The information concerning the inserted shapes is distributed on the tree’s nodes in such ...

Does there exist O(1)-competitive (self-adjusting) binary search tree (BST) algorithms? This is a well-studied problem. A simple offline BST algorithm GreedyFuture was proposed independently by Lucas [5] and Munro [6], and they conjectured it to be O(1)-competitive. Recently, Demaine et al. [2] gave a geometric view of the BST problem. This view allowed them to give an online algorithm GreedyAr...

We show that, in order to achieve efficient maintenance of a balanced binary search tree, no shape restriction other than a logarithmic height is required. The obtained class of trees, general balanced trees, may be maintained at a logarithmic amortized cost with no balance information stored in the nodes. Thus, in the case when amortized bounds are sufficient, there is no need for sophisticate...

In this paper we introduce a new algorithm for updating the parameters of a heuristic evaluation function, by updating the heuristic towards the values computed by an alpha-beta search. Our algorithm differs from previous approaches to learning from search, such as Samuel’s checkers player and the TD-Leaf algorithm, in two key ways. First, we update all nodes in the search tree, rather than a s...

Monte-Carlo Tree Search (MCTS) is a new best-first search method that started a revolution in the field of Computer Go. Parallelizing MCTS is an important way to increase the strength of any Go program. In this article, we discuss three parallelization methods for MCTS: leaf parallelization, root parallelization, and tree parallelization. To be effective tree parallelization requires two techni...

Bandit based methods for tree search have recently gained popularity when applied to huge trees, e.g. in the game of go [6]. Their efficient exploration of the tree enables to return rapidly a good value, and improve precision if more time is provided. The UCT algorithm [8], a tree search method based on Upper Confidence Bounds (UCB) [2], is believed to adapt locally to the effective smoothness...

A new contour tracking algorithm is presented. Tracking is posed as a matching problem between curves constructed out of edges in the image, and some shape space describing the class of objects of interest. The main contributions of the paper are to present an algorithm which solves this problem accurately and efficiently, in a provable manner. In particular, the algorithm’s efficiency derives ...

The design, implementation, and performance of two chess programs running on a multi-processor system are presented. Methods for distributing and enhancing the alpha-beta algorithm in a parallel environment are discussed. With the Principal Variation Splitting method, a four processor chess program yields a 3.35 fold speed-up over the sequential version. [Recreated from files dated 4 May 1984 i...

Let G be a 3-connected graph on more than 4 vertices. We show that every depth-first-search tree of G contains a contractible edge. Moreover, we show that if G is 3-regular or does not have two disjoint pairs of adjacent degree-3 vertices, every spanning tree of G contains a contractible edge.