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The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into…

Computational Complexity · Computer Science 2019-05-21 Venkatesan Guruswami , Patrick Lin

Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…

Data Structures and Algorithms · Computer Science 2018-12-10 Holger Dell , Dániel Marx

We investigate fine-grained algorithmic aspects of identification problems in graphs and set systems, with a focus on Locating-Dominating Set and Test Cover. We prove the (tight) conditional lower bounds for these problems when…

Data Structures and Algorithms · Computer Science 2025-08-25 Dipayan Chakraborty , Florent Foucaud , Diptapriyo Majumdar , Prafullkumar Tale

\textproc{Weighted Vertex Cover} is a variation of an extensively studied NP-complete problem, \textproc{Vertex Cover}, in which we are given a graph, $G = (V,E,w)$, where function $w:V \rightarrow \mathbb{Q}^{+}$ and a parameter $k$. The…

Data Structures and Algorithms · Computer Science 2020-03-25 Vishnu Veerathu , Yogesh Tripathi

Let $G$ be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. For two given list colorings of $G$, we study the problem of transforming one into…

Data Structures and Algorithms · Computer Science 2017-05-23 Tatsuhiko Hatanaka , Takehiro Ito , Xiao Zhou

The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…

Computational Complexity · Computer Science 2026-02-24 Jakub Ruszil , Artur Polański , Adam Roman , Jakub Zelek

The 3-\textsc{Hitting Set} problem is also called the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. In this paper, we address kernelizations of the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. We show that this problem…

Computational Complexity · Computer Science 2008-09-20 Xuan Cai

In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the…

Data Structures and Algorithms · Computer Science 2024-08-27 Matthias Bentert , Fedor V. Fomin , Fanny Hauser , Saket Saurabh

We study the kernel complexity of constraint satisfaction problems over a finite domain, parameterized by the number of variables, whose constraint language consists of two relations: the non-equality relation and an additional…

Computational Complexity · Computer Science 2026-04-24 Ishay Haviv

The Connected Vertex Cover problem, where the goal is to compute a minimum set of vertices in a given graph which forms a vertex cover and induces a connected subgraph, is a fundamental combinatorial problem and has received extensive…

Data Structures and Algorithms · Computer Science 2020-04-30 Diptapriyo Majumdar , M. S. Ramanujan , Saket Saurabh

We investigate the parameterized complexity of GENERALIZED RED BLUE SET COVER (Gen-RBSC), a generalization of the classic SET COVER problem and the more recently studied RED BLUE SET COVER problem. Given a universe $U$ containing $b$ blue…

Data Structures and Algorithms · Computer Science 2015-11-26 Pradeesha Ashok , Sudeshna Kolay , Saket Saurabh

We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…

Computational Complexity · Computer Science 2013-08-23 Amer E. Mouawad , Naomi Nishimura , Venkatesh Raman , Narges Simjour , Akira Suzuki

The propositional planning problem is a notoriously difficult computational problem. Downey et al. (1999) initiated the parameterized analysis of planning (with plan length as the parameter) and B\"ackstr\"om et al. (2012) picked up this…

Data Structures and Algorithms · Computer Science 2013-07-16 Christer Bäckström , Peter Jonsson , Sebastian Ordyniak , Stefan Szeider

Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…

Data Structures and Algorithms · Computer Science 2020-10-13 I. Vinod Reddy

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…

Data Structures and Algorithms · Computer Science 2023-02-02 Leon Kellerhals , Tomohiro Koana , Pascal Kunz , Rolf Niedermeier

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

Given an ordering of the vertices of a graph, the cost of covering an edge is the smaller number of its two ends. The minimum sum vertex cover problem asks for an ordering that minimizes the total cost of covering all edges. We consider…

Data Structures and Algorithms · Computer Science 2024-04-16 Yixin Cao , Ling Gai , Jingyi Liu , Jianxin Wang

In the Maximum Common Induced Subgraph problem (henceforth MCIS), given two graphs $G_1$ and $G_2$, one looks for a graph with the maximum number of vertices being both an induced subgraph of $G_1$ and $G_2$. MCIS is among the most studied…

Data Structures and Algorithms · Computer Science 2017-02-23 Faisal N. Abu-Khzam , Édouard Bonnet , Florian Sikora

In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-08-07 Ran Ben-Basat , Ken-ichi Kawarabayashi , Gregory Schwartzman

We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems…

Computational Geometry · Computer Science 2018-05-17 Jérémy Barbay , Pablo Pérez-Lantero , Javiel Rojas-Ledesma