# Nearly optimal binary search trees

@article{Mehlhorn2004NearlyOB, title={Nearly optimal binary search trees}, author={Kurt Mehlhorn}, journal={Acta Informatica}, year={2004}, volume={5}, pages={287-295} }

SummaryWe discuss two simple strategies for constructing binary search trees: “Place the most frequently occurring name at the root of the tree, then proceed similary on the subtrees “and” choose the root so as to equalize the total weight of the left and right subtrees as much as possible, then proceed similarly on the subtres.” While the former rule may yield extremely inefficient search trees, the latter rule always produces nearly optimal trees.

## 81 Citations

### New Ways to Construct Binary Search Trees

- Computer ScienceISAAC
- 2003

We give linear-time algorithms for re-ordering and height-restricting a binary search tree with only a small increase in cost, constructing a nearly optimal binary search tree given the rank by…

### Dynamic weighted binary search trees

- Computer ScienceActa Informatica
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An algorithm which optimizes a weighted binary tree after an insertion or deletion is presented, which is nearly optimal and needs O(n) space.

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- 2007

The analysis of the algorithm permits to derive a limitation on the cost of optimal binary search trees, and the obtained upper bound improve on previous results.

### Comparing Implementations of Optimal Binary Search Trees

- Computer Science
- 2017

This paper implemented five different binary search tree algorithms and compared static operations, and looked at construction time and expected depth to determine the best implementation based on number of searches before rebuilding.

### Reflections on Optimal and Nearly Optimal Binary Search Trees

- Computer ScienceEfficient Algorithms
- 2009

A rather informal look at the development of techniques for finding optimal and near optimal binary search trees and as a set of wonderful examples for teaching algorithms.

### On the max-entropy rule for a binary search tree

- Computer ScienceActa Informatica
- 2004

SummaryA modified max-entropy rule is proposed for constructing nearly optimum binary search tree in the case of ordered keys with given probabilities. The average cost of the trees obtained by this…

### Efficient Construction of Near-Optimal Binary and Multiway Search Trees

- Computer ScienceWADS
- 2009

A new linear-time algorithm for constructing multiway search trees with near-optimal search cost whose running time is independent of the size of the node in the tree and is able to provide the tightest upper bound on the average search cost for an optimal binary search tree.

### Optimum multiway search trees

- Computer ScienceActa Informatica
- 2004

A new general optimality principle is presented, which can be “tuned” for specific applications and considers the affects of three additional constraints, namely height, structural and node search restrictions, which lead to a number of new construction algorithms.

### Competitive Online Search Trees on Trees

- Computer ScienceSODA
- 2020

This work uses a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree, and describes an online $O(\log \log n)-competitive search tree data structure in this model, matching the best known competitive ratio of binary search trees.

## References

SHOWING 1-9 OF 9 REFERENCES

### Optimum binary search trees

- Computer ScienceActa Informatica
- 2004

To find if a given name is in the tree, the authors compare it to the name at the root, and four cases arise: 1. There is no root (the binary tree is empty), 2. The given name matches theName at theRoot: The search terminates suecess/ully, 3. Thegiven name is less than the nameAt the root: the search continues by examining the left subtree of the root in the same way, and 4.

### Least upper bound on the cost of optimum binary search trees

- Computer ScienceActa Informatica
- 2004

The least upper bound on the weighted path length of an optimum lexicographic (alphabetic) binary search tree as a function of n is given, given the total weight of the n terminal nodes and the n—1 internal nodes to be one.

### Bounds for Weight Balanced Trees

- Computer ScienceIBM J. Res. Dev.
- 1973

It has been shown that the cost W of a weight balanced binary tree satisfies the inequalities, H ≤ W ≤ H ≤ + 3, where H is the entropy of the set of the leaves. For a class of "smooth" distributions…

### Two applications of a probabilistic search technique: Sorting X+Y and building balanced search trees

- Computer Science, MathematicsSTOC
- 1975

It is shown that X + Y can be sorted with O(N2) comparisons and this search method translates into an insertion sort, where the insertions are not performed by means of the usual binary search, but rather as off-centered searches designed so that each comparison equally divides the space of remaining possibilities.

### The Art in Computer Programming

- Art
- 2001

Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.

### Einffihrung in die Kodierungstheorie I

- BI Skripten zur Informatik Bibliographisches Institut

### Bounds for weighted balanced trees

- IBM J. Res. Develop. March

### A top-down algorithm for constructing nearly optimal lexicographical trees, in Graph theory and Computing

- A top-down algorithm for constructing nearly optimal lexicographical trees, in Graph theory and Computing
- 1972

### Kurt Mehlhorn Fachbereich 10 Universiti~t des Saarlandes D-6600 Saarbriicken Federal Republic of Germany

- Kurt Mehlhorn Fachbereich 10 Universiti~t des Saarlandes D-6600 Saarbriicken Federal Republic of Germany