English
Related papers

Related papers: Multi-Level Steiner Trees

200 papers

We study the parameterized complexity of the directed variant of the classical {\sc Steiner Tree} problem on various classes of directed sparse graphs. While the parameterized complexity of {\sc Steiner Tree} parameterized by the number of…

Data Structures and Algorithms · Computer Science 2012-10-02 Mark Jones , Daniel Lokshtanov , M. S. Ramanujan , Saket Saurabh , Ondřej Suchý

Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…

Computational Geometry · Computer Science 2015-04-13 Stephan Held , Nicolas Kämmerling

{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…

Data Structures and Algorithms · Computer Science 2018-05-01 Davide Bilò

This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…

Data Structures and Algorithms · Computer Science 2019-05-27 Nir Bachrach , Keren Censor-Hillel , Michal Dory , Yuval Efron , Dean Leitersdorf , Ami Paz

Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…

Data Structures and Algorithms · Computer Science 2018-02-01 Mattia D'Emidio , Luca Forlizzi , Daniele Frigioni , Stefano Leucci , Guido Proietti

In recent years there has been a paradigm shift from the study of local task-related activation to the organization and functioning of large-scale functional and structural brain networks. However, a long-standing challenge in this…

Quantitative Methods · Quantitative Biology 2025-11-26 Sixtus Dakurah

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…

Networking and Internet Architecture · Computer Science 2018-03-14 Magnus M. Halldorsson , Guy Kortsarz , Pradipta Mitra , Tigran Tonoyan

Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-05-15 Suryanarayana Murthy Durbhakula

Most of the existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Therefore, we…

Machine Learning · Computer Science 2023-03-30 Jiang Xie , Shuyin Xia , Guoyin Wang , Xinbo Gao

We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations…

Statistical Mechanics · Physics 2009-01-14 M. Bayati , A. Braunstein , R. Zecchina

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.…

Artificial Intelligence · Computer Science 2021-11-25 Tobias Müller , Kyrill Schmid , Daniëlle Schuman , Thomas Gabor , Markus Friedrich , Marc Geitz

Given a weighted graph $G(V,E)$ and $t \ge 1$, a subgraph $H$ is a \emph{$t$--spanner} of $G$ if the lengths of shortest paths in $G$ are preserved in $H$ up to a multiplicative factor of $t$. The \emph{subsetwise spanner} problem aims to…

Discrete Mathematics · Computer Science 2019-04-03 Reyan Ahmed , Keaton Hamm , Mohammad Javad Latifi Jebelli , Stephen Kobourov , Faryad Darabi Sahneh , Richard Spence

Given an edge-weighted graph and a set of known seed vertices, a network scientist often desires to understand the graph relationships to explain connections between the seed vertices. When the seed set is 3 or larger Steiner minimal tree -…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-31 Tahsin Reza , Geoffrey Sanders , Roger Pearce

Network design problems aim to compute low-cost structures such as routes, trees and subgraphs. Often, it is natural and desirable to require that these structures have small hop length or hop diameter. Unfortunately, optimization problems…

Data Structures and Algorithms · Computer Science 2020-11-13 Bernhard Haeupler , D Ellis Hershkowitz , Goran Zuzic

The Steiner Tree Problem (STP) in graphs is an important problem with various applications in many areas such as design of integrated circuits, evolution theory, networking, etc. In this paper, we propose an algorithm to solve the STP. The…

Artificial Intelligence · Computer Science 2018-06-19 Matthieu De Laere , San Tu Pham , Patrick De Causmaecker

The Steiner tree problem is one of the most prominent problems in network design. Given an edge-weighted undirected graph and a subset of the vertices, called terminals, the task is to compute a minimum-weight tree containing all terminals…

Data Structures and Algorithms · Computer Science 2024-08-09 Jarosław Byrka , Fabrizio Grandoni , Vera Traub

Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…

Data Structures and Algorithms · Computer Science 2021-02-11 Bernhard Haeupler , D Ellis Hershkowitz , Goran Zuzic

Given a set of terminals in 2D/3D, the network with the shortest total length that connects all terminals is a Steiner tree. On the other hand, with enough budget, every terminal can be connected to every other terminals via a straight…

Computational Geometry · Computer Science 2022-01-28 Mario Szegedy , Jingjin Yu

In the Euclidean Steiner Tree problem, we are given as input a set of points (called terminals) in the $\ell_2$-metric space and the goal is to find the minimum-cost tree connecting them. Additional points (called Steiner points) from the…

Combinatorics · Mathematics 2023-12-05 Henry Fleischmann , Guillermo A. Gamboa Q. , Karthik C. S. , Josef Matějka , Jakub Petr

We consider network design problems with deadline or delay. All previous results for these models are based on randomized embedding of the graph into a tree (HST) and then solving the problem on this tree. We show that this is not…

Data Structures and Algorithms · Computer Science 2020-04-20 Yossi Azar , Noam Touitou