English
Related papers

Related papers: A Linear Time Parameterized Algorithm for Directed…

200 papers

There is substantial literature dealing with fixed parameter algorithms for the dominating set problem on various families of graphs. In this paper, we give a $k^{O(dk)} n$ time algorithm for finding a dominating set of size at most $k$ in…

Data Structures and Algorithms · Computer Science 2008-12-18 Noga Alon , Shai Gutner

The Directed Rural Postman Problem (DRPP) can be formulated as follows: given a strongly connected directed multigraph $D=(V,A)$ with nonnegative integral weights on the arcs, a subset $R$ of $A$ and a nonnegative integer $\ell$, decide…

Data Structures and Algorithms · Computer Science 2014-04-01 Gregory Gutin , Magnus Wahlstrom , Anders Yeo

In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…

Data Structures and Algorithms · Computer Science 2013-07-19 Yoichi Iwata , Keigo Oka , Yuichi Yoshida

{\sc Directed Feedback Vertex Set (DFVS)} is a fundamental computational problem that has received extensive attention in parameterized complexity. In this paper, we initiate the study of a wide generalization, the {\sc ${\cal H}$-free SCC…

Data Structures and Algorithms · Computer Science 2020-08-25 Rian Neogi , M. S. Ramanujan , Saket Saurabh , Roohani Sharma

Given a directed graph $G$, a set of $k$ terminals and an integer $p$, the \textsc{Directed Vertex Multiway Cut} problem asks if there is a set $S$ of at most $p$ (nonterminal) vertices whose removal disconnects each terminal from all other…

Data Structures and Algorithms · Computer Science 2015-03-19 Rajesh Chitnis , MohammadTaghi Hajiaghayi , Dániel Marx

A tournament is a directed graph T such that every pair of vertices are connected by an arc. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. In this article we consider the Feedback Vertex Set problem in…

Data Structures and Algorithms · Computer Science 2015-10-28 Mithilesh Kumar , Daniel Lokshtanov

We present a new parameterized algorithm for the {feedback vertex set} problem ({\sc fvs}) on undirected graphs. We approach the problem by considering a variation of it, the {disjoint feedback vertex set} problem ({\sc disjoint-fvs}),…

Data Structures and Algorithms · Computer Science 2014-06-04 Yixin Cao , Jianer Chen , Yang Liu

The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time $2^{O(tw)}n^{O(1)}$, for Feedback Vertex Set and connected versions of the classical…

Data Structures and Algorithms · Computer Science 2020-07-29 Benjamin Bergougnoux , Édouard Bonnet , Nick Brettell , O-joung Kwon

The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an…

Data Structures and Algorithms · Computer Science 2019-05-27 Yasuaki Kobayashi , Yusuke Kobayashi , Shuichi Miyazaki , Suguru Tamaki

We present two new deterministic algorithms for the Feedback Vertex Set problem parameterized by the solution size. We begin with a simple algorithm, which runs in O*((2 + \phi)^k) time, where \phi < 1.619 is the golden ratio. It already…

Data Structures and Algorithms · Computer Science 2013-06-18 Tomasz Kociumaka , Marcin Pilipczuk

We study the Directed Feedback Vertex Set problem parameterized by the treewidth of the input graph. We prove that unless the Exponential Time Hypothesis fails, the problem cannot be solved in time $2^{o(t\log t)}\cdot n^{\mathcal{O}(1)}$…

Data Structures and Algorithms · Computer Science 2017-09-15 Marthe Bonamy , Łukasz Kowalik , Jesper Nederlof , Michał Pilipczuk , Arkadiusz Socała , Marcin Wrochna

In the DELETION TO INDUCED MATCHING problem, we are given a graph $G$ on $n$ vertices, $m$ edges and a non-negative integer $k$ and asks whether there exists a set of vertices $S \subseteq V(G) $ such that $|S|\le k$ and the size of any…

Data Structures and Algorithms · Computer Science 2020-11-30 Akash Kumar , Mithilesh Kumar

In the Min $k$-Cut problem, input is an edge weighted graph $G$ and an integer $k$, and the task is to partition the vertex set into $k$ non-empty sets, such that the total weight of the edges with endpoints in different parts is minimized.…

Data Structures and Algorithms · Computer Science 2020-09-15 Daniel Lokshtanov , Saket Saurabh , Vaishali Surianarayanan

The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex Set (SFVS) both ask for a vertex set of minimum total weight, that for NMC disconnects a given set of terminals, and for SFVS intersects all cycles…

Data Structures and Algorithms · Computer Science 2022-01-19 Benjamin Bergougnoux , Charis Papadopoulos , Jan Arne Telle

In this paper, we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set (FVS) and Triangle Hitting (TH). We focus on the class of pseudo-disk…

Data Structures and Algorithms · Computer Science 2024-11-01 Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…

Computational Complexity · Computer Science 2026-05-05 Christian Komusiewicz , Nils Morawietz , Frank Sommer , Luca Pascal Staus

Inversion of a directed graph $D$ with respect to a vertex subset $Y$ is the directed graph obtained from $D$ by reversing the direction of every arc whose endpoints both lie in $Y$. More generally, the inversion of $D$ with respect to a…

Data Structures and Algorithms · Computer Science 2026-04-08 Dhanyamol Antony , L. Sunil Chandran , Dalu Jacob , R. B. Sandeep

At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a $2^{o(k \log k)} \cdot n^{\mathcal{O}(1)}$-time algorithm on graphs of treewidth…

Discrete Mathematics · Computer Science 2021-07-01 Hugo Jacob , Thomas Bellitto , Oscar Defrain , Marcin Pilipczuk

In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size $k$, if it exists, which runs in time $2^{O(\sqrt{k})}(n+m)$, where $n$ and $m$ denote the numbers of vertices and edges, respectively.…

Computational Geometry · Computer Science 2021-07-09 Shinwoo An , Eunjin Oh

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every…

Data Structures and Algorithms · Computer Science 2015-03-17 Dániel Marx , Igor Razgon