Related papers: Bounds and Algorithms for Alphabetic Codes and Bin…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…
This comprehensive survey examines the field of alphabetic codes, tracing their development from the 1960s to the present day. We explore classical alphabetic codes and their variants, analyzing their properties and the underlying…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…
Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…
The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally there are…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal…
In this paper, a genetic algorithm, one of the evolutionary algorithms optimization methods, is used for the first time for the problem of finding extremal binary self-dual codes. We present a comparison of the computational times between a…
The paper presents the first \emph{concurrency-optimal} implementation of a binary search tree (BST). The implementation, based on a standard sequential implementation of an internal tree, ensures that every \emph{schedule} is accepted,…
We introduce a search problem generalizing the typical setting of Binary Search on the line. Similar to the setting for Binary Search, a target is chosen adversarially on the line, and in response to a query, the algorithm learns whether…
We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring…