Related papers: Catalytic Tree Evaluation From Matching Vectors

We present a general framework for balancing expressions (terms) in form of so called tree straight-line programs. The latter can be seen as circuits over the free term algebra extended by contexts (terms with a hole) and the operations…

This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…

Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…

Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…

Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…

We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…

The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…

Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…

The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted…

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse…

The effect of training data size on machine learning methods has been well investigated over the past two decades. The predictive performance of tree based machine learning methods, in general, improves with a decreasing rate as the size of…

Tree-based machine learning techniques, such as Decision Trees and Random Forests, are top performers in several domains as they do well with limited training datasets and offer improved interpretability compared to Deep Neural Networks…

We study two fundamental decremental dynamic graph problems. In both problems, we need to maintain a vertex-weighted forest of size $n$ under edge deletions, weight updates, and a certain information-retrieval query. Both problems can be…

Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…

This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…

Label tree-based algorithms are widely used to tackle multi-class and multi-label problems with a large number of labels. We focus on a particular subclass of these algorithms that use probabilistic classifiers in the tree nodes. Examples…

Model-free forecasting of the temporal evolution of chaotic systems is crucial but challenging. Existing solutions require hyperparameter tuning, significantly hindering their wider adoption. In this work, we introduce a tree-based approach…

While Large Language Models (LLMs) have achieved remarkable success in a wide range of applications, their performance often degrades in complex reasoning tasks. In this work, we introduce SELT (Self-Evaluation LLM Tree Search), a novel…

We aim at development white-box machine learning algorithms. We focus here on algorithms for learning axioms in description logic. We extend the Class Expression Learning for Ontology Engineering (CELOE) algorithm contained in the…

Monte Carlo Tree Search (MCTS) is particularly adapted to domains where the potential actions can be represented as a tree of sequential decisions. For an effective action selection, MCTS performs many simulations to build a reliable tree…