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We study the problem of finding a minimum weight connected subgraph spanning at least $k$ vertices on planar, node-weighted graphs. We give a $(4+\eps)$-approximation algorithm for this problem. We achieve this by utilizing the recent LMP…

Data Structures and Algorithms · Computer Science 2018-05-09 Jarosław Byrka , Mateusz Lewandowski , Joachim Spoerhase

This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Nicolas Paul , Luc Fety , Michel Terre

The best algorithm for approximating Steiner tree has performance ratio $\ln(4)+\epsilon \approx 1.386$ [J. Byrka et al., \textit{Proceedings of the 42th Annual ACM Symposium on Theory of Computing (STOC)}, 2010, pp. 583-592], whereas the…

Computational Complexity · Computer Science 2017-02-21 Ali Çivril

This paper revisits the 2-approximation algorithm for $k$-MST presented by Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul et al.…

Data Structures and Algorithms · Computer Science 2023-06-21 Emmett Breen , Renee Mirka , Zichen Wang , David P. Williamson

We consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…

Data Structures and Algorithms · Computer Science 2019-09-24 Evripidis Bampis , Bruno Escoffier , Alexander Kononov

The Steiner Forest problem is an important generalization of the Steiner Tree problem. We are given an undirected graph with nonnegative edge costs and a collection of pairs of vertices. The task is to compute a cheapest forest with the…

Data Structures and Algorithms · Computer Science 2024-12-10 Jarosław Byrka , Fabrizio Grandoni , Vera Traub

We present an approximation algorithm for the Prize-collecting Ordered Traveling Salesman Problem (PCOTSP), which simultaneously generalizes the Prize-collecting TSP and the Ordered TSP. The Prize-collecting TSP is well-studied and has a…

Data Structures and Algorithms · Computer Science 2024-11-25 Morteza Alimi , Tobias Mömke , Michael Ruderer

We present a simple 4-approximation algorithm for computing a maximum agreement forest of multiple unrooted binary trees. This algorithm applies LP rounding to an extension of a recent ILP formulation of the maximum agreement forest problem…

Data Structures and Algorithms · Computer Science 2024-09-16 Jordan Dempsey , Leo van Iersel , Mark Jones , Norbert Zeh

There is a large discrepancy in our understanding of uncapacitated and capacitated versions of network location problems. This is perhaps best illustrated by the classical k-center problem: there is a simple tight 2-approximation algorithm…

Data Structures and Algorithms · Computer Science 2013-04-11 Hyung-Chan An , Aditya Bhaskara , Ola Svensson

We design a 3/2 approximation algorithm for the Generalized Steiner Tree problem (GST) in metrics with distances 1 and 2. This is the first polynomial time approximation algorithm for a wide class of non-geometric metric GST instances with…

Computational Complexity · Computer Science 2008-12-12 Piotr Berman , Marek Karpinski , Alex Zelikovsky

Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$ Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and some (or none or all) points of $S$. A Steiner tree with length of longest edge…

Computational Geometry · Computer Science 2010-12-08 A. Karim Abu-Affash

We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned…

Data Structures and Algorithms · Computer Science 2026-03-02 Nate Veldt , Thomas Stanley , Benjamin W. Priest , Trevor Steil , Keita Iwabuchi , T. S. Jayram , Grace J. Li , Geoffrey Sanders

We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The…

Data Structures and Algorithms · Computer Science 2013-09-18 Piotr Skowron , Piotr Faliszewski

In the unsplittable capacitated vehicle routing problem (UCVRP) on trees, we are given a rooted tree with edge weights and a subset of vertices of the tree called terminals. Each terminal is associated with a positive demand between 0 and…

Data Structures and Algorithms · Computer Science 2022-11-09 Claire Mathieu , Hang Zhou

We are given n base elements and a finite collection of subsets of them. The size of any subset varies between p to k (p < k). In addition, we assume that the input contains all possible subsets of size p. Our objective is to find a…

Data Structures and Algorithms · Computer Science 2009-06-09 Asaf Levin , Uri Yovel

In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…

Data Structures and Algorithms · Computer Science 2015-12-10 Stephan Beyer , Markus Chimani

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…

Data Structures and Algorithms · Computer Science 2018-08-08 Takuro Fukunaga , Takanori Maehara

In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\{c_e\geq 0\}_{e\in E}$, terminal pairs $\{(s_i,t_i)\}_{i=1}^k$, and penalties $\{\pi_i\}_{i=1}^k$ for each terminal pair; the…

Discrete Mathematics · Computer Science 2017-06-21 Jochen Könemann , Neil Olver , Kanstantsin Pashkovich , R. Ravi , Chaitanya Swamy , Jens Vygen

Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…

Data Structures and Algorithms · Computer Science 2025-07-31 Josefine Foos , Stephan Held , Yannik Kyle Dustin Spitzley

We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced…

Data Structures and Algorithms · Computer Science 2024-10-08 Martin Frohn , Steven Kelk , Simona Vychytilova