Related papers: HyperSteiner: Computing Heuristic Hyperbolic Stein…
We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
A spanning tree $T$ of graph $G$ is a $\rho$-approximate universal Steiner tree (UST) for root vertex $r$ if, for any subset of vertices $S$ containing $r$, the cost of the minimal subgraph of $T$ connecting $S$ is within a $\rho$ factor of…
We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based…
Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…
An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error e from 120 degrees.This notion arises in numerical approximations of…
The expansion of Fiber-To-The-Home (FTTH) networks creates high costs due to expensive excavation procedures. Optimizing the planning process and minimizing the cost of the earth excavation work therefore lead to large savings.…
The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature…
Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…
Motivation: Navigating the high dimensional space of discrete trees for phylogenetics presents a challenging problem for tree optimisation. To address this, hyperbolic embeddings of trees offer a promising approach to encoding trees…
We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…
We consider the bilevel minimum spanning tree (BMST) problem where the leader and the follower choose a spanning tree together, according to different objective functions. By showing that this problem is NP-hard in general, we answer an…
The prevalence of tree-like structures, encompassing hierarchical structures and power law distributions, exists extensively in real-world applications, including recommendation systems, ecosystems, financial networks, social networks, etc.…
Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute…
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural…