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The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…

Computational Geometry · Computer Science 2023-12-01 T-H. Hubert Chan , Gramoz Goranci , Shaofeng H. -C. Jiang , Bo Wang , Quan Xue

In the k-edge connected directed Steiner tree (k-DST) problem, we are given a directed graph G on n vertices with edge-costs, a root vertex r, a set of h terminals T and an integer k. The goal is to find a min-cost subgraph H of G that…

Data Structures and Algorithms · Computer Science 2016-03-01 Bundit Laekhanukit

Given a set $P$ of $n$ points in $\mathbb{R}^2$ and an input line $\gamma$ in $\mathbb{R}^2$, we present an algorithm that runs in optimal $\Theta(n\log n)$ time and $\Theta(n)$ space to solve a restricted version of the $1$-Steiner tree…

Computational Geometry · Computer Science 2023-06-16 Prosenjit Bose , Anthony D'Angelo , Stephane Durocher

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Data Structures and Algorithms · Computer Science 2010-06-18 Marek Cygan , Lukasz Kowalik , Marcin Mucha , Marcin Pilipczuk , Piotr Sankowski

The Euclidean Steiner tree problem seeks the min-cost network to connect a collection of target locations, and it underlies many applications of wireless networks. In this paper, we present a study on solving the Euclidean Steiner tree…

Machine Learning · Computer Science 2022-09-22 Siqi Wang , Yifan Wang , Guangmo Tong

Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant on the well-known Christofides' algorithm for the TSP, called the Best-of-Many Christofides' algorithm. The algorithm involves…

Data Structures and Algorithms · Computer Science 2015-06-26 Kyle Genova , David P. Williamson

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is…

Data Structures and Algorithms · Computer Science 2016-11-23 Eric Angel , Nguyen Kim Thang , Shikha Singh

Given a graph G, the {\em maximum internal spanning tree problem} (MIST for short) asks for computing a spanning tree T of G such that the number of internal vertices in T is maximized. MIST has possible applications in the design of…

Data Structures and Algorithms · Computer Science 2016-08-02 Zhi-Zhong Chen , Youta Harada , Lusheng Wang

Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…

Data Structures and Algorithms · Computer Science 2025-02-19 Nate Veldt , Thomas Stanley , Benjamin W. Priest , Trevor Steil , Keita Iwabuchi , T. S. Jayram , Geoffrey Sanders

The Belief Propagation approximation, or cavity method, has been recently applied to several combinatorial optimization problems in its zero-temperature implementation, the max-sum algorithm. In particular, recent developments to solve the…

Data Structures and Algorithms · Computer Science 2019-01-04 Alfredo Braunstein , Anna Paola Muntoni

This paper investigates the problem of regression model generation. A model is a superposition of primitive functions. The model structure is described by a weighted colored graph. Each graph vertex corresponds to some primitive function.…

Machine Learning · Statistics 2024-06-28 Radoslav G. Neychev , Innokentiy A. Shibaev , Vadim V. Strijov

The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point…

Systems and Control · Electrical Eng. & Systems 2026-04-24 Manou Rosenberg , Mengbin Ye , Brian D. O. Anderson

We consider the following general network design problem on directed graphs. The input is an asymmetric metric $(V,c)$, root $r^{*}\in V$, monotone submodular function $f:2^V\rightarrow \mathbb{R}_+$ and budget $B$. The goal is to find an…

Data Structures and Algorithms · Computer Science 2019-04-03 Rohan Ghuge , Viswanath Nagarajan

We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network…

Data Structures and Algorithms · Computer Science 2017-07-12 Guru Guruganesh , Jennifer Iglesias , R. Ravi , Laura Sanità

We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the…

Computational Geometry · Computer Science 2007-05-23 Josiah Carlson , David Eppstein

We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…

Data Structures and Algorithms · Computer Science 2025-04-24 Jiwei Zhang , Deepak Ajwani

We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…

Data Structures and Algorithms · Computer Science 2023-02-24 Magnus Berg , Joan Boyar , Lene M. Favrholdt , Kim S. Larsen

In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path…

Data Structures and Algorithms · Computer Science 2022-11-10 Stephan Held , Yannik Kyle Dustin Spitzley

The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…

Data Structures and Algorithms · Computer Science 2011-02-25 Anupam Gupta , Viswanath Nagarajan , R. Ravi

The Steiner Forest problem, also known as the Generalized Steiner Tree problem, is a fundamental optimization problem on edge-weighted graphs where, given a set of vertex pairs, the goal is to select a minimum-cost subgraph such that each…

Data Structures and Algorithms · Computer Science 2025-04-16 Ali Ahmadi , Iman Gholami , MohammadTaghi Hajiaghayi , Peyman Jabbarzade , Mohammad Mahdavi