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Related papers: Approximations for the Steiner Multicycle Problem

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We present an algorithm for the asymmetric traveling salesman problem on instances which satisfy the triangle inequality. Like several existing algorithms, it achieves approximation ratio O(log n). Unlike previous algorithms, it uses…

Data Structures and Algorithms · Computer Science 2009-09-07 Michel X. Goemans , Nicholas J. A. Harvey , Kamal Jain , Mohit Singh

We study two problems that seek a subtree $T$ of a graph $G=(V,E)$ such that $T$ satisfies a certain property and has minimal maximum degree. - In the Min-Degree Group Steiner Tree problem we are given a collection ${\cal S}$ of groups…

Data Structures and Algorithms · Computer Science 2019-10-29 Guy Kortsarz , Zeev Nutov

Given an undirected node-weighted graph, the Maximum-Weight Connected Subgraph problem (MWCS) is to identify a subset of nodes of maximalsum of weights that induce a connected subgraph. MWCS is closely related to the well-studied Prize…

Data Structures and Algorithms · Computer Science 2014-12-03 Mohammed El-Kebir , Gunnar W. Klau

In the maximum scatter traveling salesman problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting…

Discrete Mathematics · Computer Science 2017-07-17 Isabella Hoffmann , Sascha Kurz , Jörg Rambau

We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: we construct the greedy multi-fragment tour for…

Computational Geometry · Computer Science 2019-12-04 Nil Mamano , Alon Efrat , David Eppstein , Daniel Frishberg , Michael Goodrich , Stephen Kobourov , Pedro Matias , Valentin Polishchuk

Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…

Data Structures and Algorithms · Computer Science 2016-11-08 Guilherme D. da Fonseca , Vinícius G. Pereira de Sá , Celina M. H. de Figueiredo

We give approximation schemes for Subset TSP and Steiner Tree on unit disk graphs, and more generally, on intersection graphs of similarly sized connected fat (not necessarily convex) polygons in the plane. As a first step towards this…

Data Structures and Algorithms · Computer Science 2026-03-30 Sándor Kisfaludi-Bak , Dániel Marx

We present polylogarithmic approximation algorithms for variants of the Shortest Path, Group Steiner Tree, and Group ATSP problems with vector costs. In these problems, each edge e has a non-negative vector cost $c_e \in…

Data Structures and Algorithms · Computer Science 2024-04-30 Yury Makarychev , Max Ovsiankin , Erasmo Tani

Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…

Data Structures and Algorithms · Computer Science 2009-05-28 Greg N. Frederickson , Barry Wittman

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…

Data Structures and Algorithms · Computer Science 2015-07-03 MohammadTaghi Hajiaghayi , Guy Kortsarz , Robert MacDavid , Manish Purohit , Kanthi Sarpatwar

In a directed graph $G$ with non-correlated edge lengths and costs, the \emph{network design problem with bounded distances} asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria…

Data Structures and Algorithms · Computer Science 2014-09-24 Markus Chimani , Joachim Spoerhase

Local search is a widely-employed strategy for finding good solutions to Traveling Salesman Problem. We analyze the problem of determining whether the weight of a given cycle can be decreased by a popular $k$-opt move. Earlier work has…

Data Structures and Algorithms · Computer Science 2019-09-04 Édouard Bonnet , Yoichi Iwata , Bart M. P. Jansen , Łukasz Kowalik

We use the Stein-Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical…

Probability · Mathematics 2019-04-05 Matthew Coulson , Robert E. Gaunt , Gesine Reinert

Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…

Data Structures and Algorithms · Computer Science 2015-10-01 Glencora Borradaile , Philip Klein

Locating source of diffusion in networks is crucial for controlling and preventing epidemic risks. It has been studied under various probabilistic models. In this paper, we study source location from a deterministic point of view by…

Discrete Mathematics · Computer Science 2014-04-21 Xujin Chen , Xiaodong Hu , Changjun Wang

We present a fast combinatorial $3/4$-approximation algorithm for the maximum asymmetric TSP with weights zero and one. The approximation factor of this algorithm matches the currently best one given by Bl\"aser in 2004 and based on linear…

Data Structures and Algorithms · Computer Science 2014-08-08 Katarzyna Paluch

In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-13 Lélia Blin , Maria Gradinariu Potop-Butucaru , Stephane Rovedakis

One of the most studied extensions of the famous Traveling Salesperson Problem (TSP) is the {\sc Multiple TSP}: a set of $m\geq 1$ salespersons collectively traverses a set of $n$ cities by $m$ non-trivial tours, to minimize the total…

Data Structures and Algorithms · Computer Science 2023-07-17 Max Deppert , Matthias Kaul , Matthias Mnich

The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper 10.1016/j.ejor.2014.05.042, the…

Data Structures and Algorithms · Computer Science 2016-07-19 William W. Hager , James T. Hungerford , Ilya Safro

In the Steiner Forest problem, we are given a graph with edge lengths, and a collection of demand pairs; the goal is to find a subgraph of least total length such that each demand pair is connected in this subgraph. For over twenty years,…

Data Structures and Algorithms · Computer Science 2025-11-25 Anupam Gupta , Vera Traub