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Graph Burning asks, given a graph $G = (V,E)$ and an integer $k$, whether there exists $(b_{0},\dots,b_{k-1}) \in V^{k}$ such that every vertex in $G$ has distance at most $i$ from some $b_{i}$. This problem is known to be NP-complete even…

Data Structures and Algorithms · Computer Science 2020-09-29 Yasuaki Kobayashi , Yota Otachi

We investigate structural parameterizations of two identification problems: LOCATING-DOMINATING SET and TEST COVER. In the first problem, an input is a graph $G$ on $n$ vertices and an integer $k$, and one asks if there is a subset $S$ of…

Data Structures and Algorithms · Computer Science 2024-11-28 Dipayan Chakraborty , Florent Foucaud , Diptapriyo Majumdar , Prafullkumar Tale

In the Vertex Cover problem we are given a graph $G=(V,E)$ and an integer $k$ and have to determine whether there is a set $X\subseteq V$ of size at most $k$ such that each edge in $E$ has at least one endpoint in $X$. The problem can be…

Data Structures and Algorithms · Computer Science 2016-11-22 Stefan Kratsch

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

We investigate the parameterized complexity of Vertex Cover parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change…

Data Structures and Algorithms · Computer Science 2012-03-14 Daniel Lokshtanov , N. S. Narayanaswamy , Venkatesh Raman , M. S. Ramanujan , Saket Saurabh

An important result in the study of polynomial-time preprocessing shows that there is an algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at…

Data Structures and Algorithms · Computer Science 2015-03-17 Bart M. P. Jansen , Hans L. Bodlaender

We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…

Data Structures and Algorithms · Computer Science 2025-12-09 Tesshu Hanaka , Yuto Okada , Yota Otachi , Lena Volk

The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…

Computational Complexity · Computer Science 2013-07-25 Christian Knauer , Stefan König , Daniel Werner

We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by…

Discrete Mathematics · Computer Science 2015-09-02 Bjarki Ágúst Guðmundsson , Tómas Ken Magnússon , Björn Orri Sæmundsson

We complement the recent algorithmic result that Feedback Vertex Set is XP-time solvable parameterized by the mim-width of a given branch decomposition of the input graph [3] by showing that the problem is W[1]-hard in this…

Computational Complexity · Computer Science 2017-11-15 Lars Jaffke , O-joung Kwon , Jan Arne Telle

In this paper we give a f-approximation algorithm for the minimum unweighted Vertex Cover problem with Hard Capacity constraints (VCHC) on f-hypergraphs. This problem generalizes standard vertex cover for which the best known approximation…

Data Structures and Algorithms · Computer Science 2017-01-24 Sam Chiu-wai Wong

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…

Discrete Mathematics · Computer Science 2015-12-04 Jiří Fiala , Tomáš Gavenčiak , Dušan Knop , Martin Koutecký , Jan Kratochvíl

We study the problem of Imbalance parameterized by the twin cover of a graph. We show that Imbalance is XP parameterized by twin cover, and FPT when parameterized by the twin cover and the size of the largest clique outside the twin cover.…

Data Structures and Algorithms · Computer Science 2020-05-11 Neeldhara Misra , Harshil Mittal

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…

Data Structures and Algorithms · Computer Science 2018-12-18 Michael J. Bannister , Sergio Cabello , David Eppstein

A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a…

Data Structures and Algorithms · Computer Science 2019-08-26 Sujoy Bhore , Robert Ganian , Fabrizio Montecchiani , Martin Nöllenburg

We study a recently introduced generalization of the Vertex Cover (VC) problem, called Power Vertex Cover (PVC). In this problem, each edge of the input graph is supplied with a positive integer demand. A solution is an assignment of…

Data Structures and Algorithms · Computer Science 2023-06-22 Eric Angel , Evripidis Bampis , Bruno Escoffier , Michael Lampis

Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the…

Data Structures and Algorithms · Computer Science 2012-01-18 Robert Ganian

The Firefighter problem is to place firefighters on the vertices of a graph to prevent a fire with known starting point from lighting up the entire graph. In each time step, a firefighter may be permanently placed on an unburned vertex and…

Discrete Mathematics · Computer Science 2011-09-23 Marek Cygan , Fedor V. Fomin , Erik Jan van Leeuwen

In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…

Data Structures and Algorithms · Computer Science 2023-06-08 Chien-Chung Huang , François Sellier

In the Mixed Chinese Postman Problem (MCPP), given a weighted mixed graph $G$ ($G$ may have both edges and arcs), our aim is to find a minimum weight closed walk traversing each edge and arc at least once. The MCPP parameterized by the…

Computational Complexity · Computer Science 2015-01-27 Gregory Gutin , Mark Jones , Magnus Wahlstrom