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In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…

Data Structures and Algorithms · Computer Science 2024-06-03 N. R. Aravind , Roopam Saxena

The NP-hard Metric Dimension problem is to decide for a given graph G and a positive integer k whether there is a vertex subset of size at most k that separates all vertex pairs in G. Herein, a vertex v separates a pair {u,w} if the…

Computational Complexity · Computer Science 2012-11-08 Sepp Hartung , André Nichterlein

We study the problem Symmetric Directed Multicut from a parameterized complexity perspective. In this problem, the input is a digraph $D$, a set of cut requests $C=\{(s_1,t_1),\ldots,(s_\ell,t_\ell)\}$ and an integer $k$, and the task is to…

Data Structures and Algorithms · Computer Science 2022-08-22 Eduard Eiben , Clément Rambaud , Magnus Wahlström

The classical Feedback Vertex Set problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. Feedback Vertex Set has attracted a large amount of research in…

Data Structures and Algorithms · Computer Science 2011-08-02 Marek Cygan , Marcin Pilipczuk , Michal Pilipczuk , Jakub Onufry Wojtaszczyk

In this paper, we study several coloring problems on graphs from the viewpoint of parameterized complexity. We show that Precoloring Extension is fixed-parameter tractable (FPT) parameterized by distance to clique and Equitable Coloring is…

Data Structures and Algorithms · Computer Science 2020-05-29 I. Vinod Reddy

We prove algorithmic results showing that a number of natural parameterized problems are in the restricted-space parameterized classes Para-L and FPT+XL. The first class comprises problems solvable in f(k) n^{O(1)} time using g(k) + O(log…

Data Structures and Algorithms · Computer Science 2022-01-03 Arindam Biswas , Venkatesh Raman , Srinivasa Rao Satti , Saket Saurabh

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters…

Discrete Mathematics · Computer Science 2015-05-18 Mong-Jen Kao , Han-Lin Chen

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…

Computational Geometry · Computer Science 2015-02-18 Panos Giannopoulos , Christian Knauer , Gunter Rote , Daniel Werner

An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…

Data Structures and Algorithms · Computer Science 2021-01-20 Louis Dublois , Michael Lampis , Vangelis Th. Paschos

We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…

Data Structures and Algorithms · Computer Science 2024-07-26 Tim Randolph , Karol Węgrzycki

A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs.…

Data Structures and Algorithms · Computer Science 2012-05-17 Nicolas Bousquet , Daniel Gonçalves , George B. Mertzios , Christophe Paul , Ignasi Sau , Stéphan Thomassé

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

We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set. Given a red-blue bipartite graph $G$ and an auxiliary connectivity graph $G_{conn}$ on red vertices, and integers $k, t$, the…

Data Structures and Algorithms · Computer Science 2026-01-14 Tanmay Inamdar , Satyabrata Jana , Madhumita Kundu , Daniel Lokshtanov , Saket Saurabh , Meirav Zehavi

We consider scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than $1.5$…

Data Structures and Algorithms · Computer Science 2017-01-26 Klaus Jansen , Marten Maack , Roberto Solis-Oba

This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…

Data Structures and Algorithms · Computer Science 2009-09-11 David Eppstein

The Minimum Vertex Cover problem, a classical NP-complete problem, presents significant challenges for exact solution on large graphs. Fixed-Parameter Tractability (FPT) offers a powerful paradigm to address such problems by exploiting a…

Data Structures and Algorithms · Computer Science 2025-07-15 Mumuksh Tayal

For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on…

Data Structures and Algorithms · Computer Science 2025-03-18 Florent Foucaud , Esther Galby , Liana Khazaliya , Shaohua Li , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at…

Computational Complexity · Computer Science 2015-06-11 Cristina Bazgan , Morgan Chopin , André Nichterlein , Florian Sikora

We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional…

Data Structures and Algorithms · Computer Science 2020-03-17 Nikolaos Melissinos , Aris Pagourtzis , Theofilos Triommatis

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