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...

This paper presents a combinational quantum-inspired binary gravitational search algorithm (QBGSA) for solving the optimal power quality monitor (PQM) placement problem in power systems for voltage sag assessment. In this algorithm, the standard binary gravitational search algorithm is modified by applying the concept and principles of quantum behaviour as to improve the search capability with ...

We propose a simple modification to the recently proposed compressive binary search [1]. The modification removes an unnecessary and suboptimal factor of log log n from the SNR requirement, making the procedure optimal (up to a small constant). Simulations show that the new procedure performs significantly better in practice as well. We also contrast this problem with the well known noisy binar...

We present a new linear time heuristic for constructing binary search trees. The analysis of the algorithm, by establishing an upper bound on the cost of the produced binary search trees, permits to derive a limitation on the cost of optimal binary search trees. The obtained upper bound improve on previous results.

We present a general method for de-amortizing essentially any Binary Search Tree (BST) algorithm. In particular, by transforming Splay Trees, our method produces a BST that has the same asymptotic cost as Splay Trees on any access sequence while performing each search in O(log n) worst case time. By transforming Multi-Splay Trees, we obtain a BST that is O(log log n) competitive, satisfies the ...

We revisit the classical problem of searching in a binary search tree (BST) using rotations, and present novel connections of this problem to a number of geometric and combinatorial structures. In particular, we show that the execution trace of a BST that serves a sequence of queries is in close correspondence with the flip-sequence between two rectangulations. (Rectangulations are well-studied...