Related papers: Catalytic Tree Evaluation From Matching Vectors
We give an algorithm that takes as input an $n$-vertex graph $G$ and an integer $k$, runs in time $2^{O(k^2)} n^{O(1)}$, and outputs a tree decomposition of $G$ of width at most $k$, if such a decomposition exists. This resolves the…
We provide the first algorithm for computing an optimal tree decomposition for a given graph $G$ that runs in single exponential time in the feedback vertex number of $G$, that is, in time $2^{O(\text{fvn}(G))}\cdot n^{O(1)}$, where…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and programs with high complexity or on…
The width measure \emph{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. We present an algorithm which---given as input…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
Competition-level code generation tasks pose significant challenges for current state-of-the-art large language models (LLMs). For example, on the LiveCodeBench-Hard dataset, models such as O1-Mini and O1-Preview achieve pass@1 rates of…
We study quantum algorithms on search trees of unknown structure, in a model where the tree can be discovered by local exploration. That is, we are given the root of the tree and access to a black box which, given a vertex $v$, outputs the…
We show fast deterministic algorithms for fundamental problems on forests in the challenging low-space regime of the well-known Massive Parallel Computation (MPC) model. A recent breakthrough result by Coy and Czumaj [STOC'22] shows that,…
There is a rising interest in mapping trees using satellite or aerial imagery, but there is no standardized evaluation protocol for comparing and enhancing methods. In dense canopy areas, the high variability of tree sizes and their spatial…
Recent advances in machine learning and artificial intelligence are now being considered in safety-critical autonomous systems where software defects may cause severe harm to humans and the environment. Design organizations in these domains…
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…
We show how to construct a dynamic ordered dictionary, supporting insert/delete/rank/select on a set of $n$ elements from a universe of size $U$, that achieves the optimal amortized expected time complexity of $O(1 + \log n / \log \log U)$,…
The Tree Evaluation Problem was introduced by Cook et al. in 2010 as a candidate for separating P from L and NL. The most general space lower bounds known for the Tree Evaluation Problem require a semantic restriction on the branching…
Modern language models address complex questions through chain-of-thought (CoT) reasoning (Wei et al., 2023) and retrieval augmentation (Lewis et al., 2021), yet struggle with error propagation and knowledge integration. Tree-structured…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
We give the first {\sl reconstruction algorithm} for decision trees: given queries to a function $f$ that is $\mathrm{opt}$-close to a size-$s$ decision tree, our algorithm provides query access to a decision tree $T$ where: $\circ$ $T$ has…
Tree kernels have been proposed to be used in many areas as the automatic learning of natural language applications. In this paper, we propose a new linear time algorithm based on the concept of weighted tree automata for SubTree kernel…
Reinforcement learning (RL) with tree search has demonstrated superior performance in traditional reasoning tasks. Compared to conventional independent chain sampling strategies with outcome supervision, tree search enables better…
Deliberative tree search is a cornerstone of modern Large Language Model (LLM) research, driving the pivot from brute-force scaling toward algorithmic efficiency. This single paradigm unifies two critical frontiers: \textbf{Test-Time…