Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let hmin(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal binary search tree with near minimal height, i.e. with height h ≤ hmin(n) +∆ for some fixed ∆. It is shown, that for any fixed∆ optimal binary search trees wi...

We give linear-time algorithms for re-ordering and heightrestricting a binary search tree with only a small increase in cost, constructing a nearly optimal binary search tree given the rank by probability of each possible outcome, and height-restricting an optimal binary search tree when the increase in cost is restricted. Whereas most algorithms for constructing good binary search trees need t...

II Binary search 4 II-A Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 II-B Binary search with stretch-intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 II-B.1 Within a stretch-interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 II-B.2 Binary search among stretch intervals . . . . . . . . . . . ...

We consider random binary search trees when the input consists of a multiset, i.e. a set with multiple occurrences of equal elements, and prove that the randomized insertion and deletion algorithms produce random search trees regardless of multiplicities; even if all the elements are equal during the tree updates, a search tree will maintain its randomness. Thus, equal elements do not degenerat...

Binary Search Trees are a frequently used data structure for rapid access to the stored data. Data structures like arrays, vectors and linked lists are limited by the trade-off between the ability to perform a fast search and resize easily. They are an alternative that is both dynamic in size and easily searchable. Due to efficiency reason, complete and nearly complete binary search trees are o...

In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...