Related papers: On the Tree Search Problem with Non-uniform Costs

Decision Tree is a classic formulation of active learning: given $n$ hypotheses with nonnegative weights summing to 1 and a set of tests that each partition the hypotheses, output a decision tree using the provided tests that uniquely…

A mobile agent has to find an inert target in some environment that can be a graph or a terrain in the plane. This task is known as treasure hunt. We consider deterministic algorithms for treasure hunt in trees. Our goal is to establish the…

We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…

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…

We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…

The graph invariant EPT-sum has cropped up in several unrelated fields in later years: As an objective function for hierarchical clustering, as a more fine-grained version of the classical edge ranking problem, and, specifically when the…

We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…

Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…

Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to…

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

Tree search has recently emerged as a powerful framework for aligning generative models with task-specific rewards at test time. Applying tree search to Masked Diffusion Language Models, however, introduces two key challenges: (i) parallel…

We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…

We study the query complexity of the metric Steiner Tree problem, where we are given an $n \times n$ metric on a set $V$ of vertices along with a set $T \subseteq V$ of $k$ terminals, and the goal is to find a tree of minimum cost that…

Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…

We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…

Given a complete graph $G=(V,E)$, with nonnegative edge costs, two subsets $R \subset V$ and $R^{\prime} \subset R$, a partition $\mathcal{R}=\{R_1,R_2,\ldots,R_k\}$ of $R$, $R_i \cap R_j=\phi$, $i \neq j$ and…

A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…

We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…