Related papers: A Simple Balanced Search Tree with No Balance Crit…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Nonlinear optimization methods are typically iterative and make use of gradient information to determine a direction of improvement and function information to effectively check for progress. When this information is corrupted by noise,…

This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses…

We revisit weight-balanced trees, also known as trees of bounded balance. This class of binary search trees was invented by Nievergelt and Reingold in 1972. Such trees are obtained by assigning a weight to each node and requesting that the…

A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. However, this method is limited in the sense that its redundancy is twice that of the full sets of balanced codes. The gap between…

Tree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are…

We present an algorithm that allows for find-closest-point and kNN-style traversals of left-balanced k-d trees, without the need for either recursion or software-managed stacks; instead using only current and last previously traversed node…

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…

Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts.…

In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…

In this paper we present a subgradient method with non-monotone line search for the minimization of convex functions with simple convex constraints. Different from the standard subgradient method with prefixed step sizes, the new method…

We introduce and analyze two parameter-free linear-memory tree search algorithms. Under mild assumptions we prove our algorithms are guaranteed to perform only a logarithmic factor more node expansions than A* when the search space is a…

We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…

This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…

The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…

Nowadays, multiprocessing is mainstream with exponentially increasing number of processors. Load balancing is, therefore, a critical operation for the efficient execution of parallel algorithms. In this paper we consider the fundamental…

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…

Tree balance plays an important role in various research areas in phylogenetics and computer science. Typically, it is measured with the help of a balance index or imbalance index. There are more than 25 such indices available, recently…

We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…

In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…