Related papers: Fast Rational Search via Stern-Brocot Tree

A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root…

We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest…

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown…

We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…

Bandit based methods for tree search have recently gained popularity when applied to huge trees, e.g. in the game of go [6]. Their efficient exploration of the tree enables to re- turn rapidly a good value, and improve preci- sion if more…

The vast amounts of data collected in various domains pose great challenges to modern data exploration and analysis. To find "interesting" objects in large databases, users typically define a query using positive and negative example…

Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixed-depth minimax tree-search algorithm traversing a uniform tree must explore, the so-called minimal tree. Since real-life minimax trees are not…

Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…

Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…

While chain-of-thought prompting with Best-of-N (BoN) selection has become popular for mathematical reasoning in large language models (LLMs), its linear structure fails to capture the branching and exploratory nature of complex…

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…

Uncertainty arises naturally inmany application domains due to, e.g., data entry errors and ambiguity in data cleaning. Prior work in incomplete and probabilistic databases has investigated the semantics and efficient evaluation of ranking…

There are two well-known ways to enumerate the positive rational numbers in an infinite binary tree: the Farey/Stern-Brocot tree and the Calkin-Wilf tree. In this brief note, we describe these two trees as `transpose shadows' of a tree of…

The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…

We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of…

Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…

Designing search algorithms for finding global optima is one of the most active research fields, recently. These algorithms consist of two main categories, i.e., classic mathematical and metaheuristic algorithms. This article proposes a…

The personnel rostering problem is the problem of finding an optimal way to assign employees to shifts, subject to a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative…

Motivated by programmatic advertising optimization, we consider the task of sequentially allocating budget across a set of resources. At every time step, a feasible allocation is chosen and only a corresponding random return is observed.…

We introduce two novel tree search algorithms that use a policy to guide search. The first algorithm is a best-first enumeration that uses a cost function that allows us to prove an upper bound on the number of nodes to be expanded before…