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We give an algorithm that takes as input an $n$-vertex graph $G$ and an integer $k$, runs in time $2^{O(k^2)} n^{O(1)}$, and outputs a tree decomposition of $G$ of width at most $k$, if such a decomposition exists. This resolves the…

Data Structures and Algorithms · Computer Science 2023-08-21 Tuukka Korhonen , Daniel Lokshtanov

We obtain polynomial-time approximation-preserving reductions (up to a factor of 1 + \epsilon) from the prize-collecting Steiner tree and prize-collecting Steiner forest problems in planar graphs to the corresponding problems in graphs of…

Data Structures and Algorithms · Computer Science 2010-06-23 Chandra Chekuri , Alina Ene , Nitish Korula

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

Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…

Data Structures and Algorithms · Computer Science 2016-05-17 Frank Kammer , Torsten Tholey

We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently:…

Discrete Mathematics · Computer Science 2025-02-19 Hans L. Bodlaender , Carla Groenland , Hugo Jacob

We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…

Data Structures and Algorithms · Computer Science 2021-07-19 Julián Mestre , Sergey Pupyrev , Seeun William Umboh

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 consider connectivity problems with orientation constraints. Given a directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]=\{(u,v) \in P: D {contains a} uv{-path}}$. In the {\sf Steiner Forest Orientation} problem we…

Data Structures and Algorithms · Computer Science 2012-07-19 Marek Cygan , Guy Kortsarz , Zeev Nutov

Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…

Computational Complexity · Computer Science 2022-12-20 Falko Hegerfeld , Stefan Kratsch

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 this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euclidean plane and the lengths are Euclidean distances. First,…

Data Structures and Algorithms · Computer Science 2009-12-08 MohammadHossein Bateni , MohammadTaghi Hajiaghayi

Many problems are known to be solvable in subexponential parameterized time when the input graph is planar. The bidimensionality framework of Demaine, Fomin, Hajiaghay, and Thilikos [JACM'05] and the treewidth-pattern-covering approach by…

Data Structures and Algorithms · Computer Science 2026-04-02 Matthias Bentert , Fedor V. Fomin , Petr A. Golovach

{\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

Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms.…

Data Structures and Algorithms · Computer Science 2025-05-15 Niko Hastrich , Kirill Simonov

In this paper, we develop a new parameterized algorithm for the {\sc Independent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, the goal of the problem is to determine whether there exists a vertex subset $F\subseteq V$ such…

Data Structures and Algorithms · Computer Science 2013-08-02 Yinglei Song

We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…

Data Structures and Algorithms · Computer Science 2016-10-26 Dániel Marx , Marcin Pilipczuk

Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex…

Computational Complexity · Computer Science 2018-08-21 Benjamin Bergougnoux , Mamadou Moustapha Kanté

We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a…

Data Structures and Algorithms · Computer Science 2009-09-18 Neeldhara Misra , Geevarghese Philip , Venkatesh Raman , Saket Saurabh , Somnath Sikdar

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…

Data Structures and Algorithms · Computer Science 2016-10-05 Thomas Bosman

We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…

Data Structures and Algorithms · Computer Science 2022-06-24 Mahdi Belbasi , Martin Fürer