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In a large-scale network, we want to choose some influential nodes to make a profit by paying some cost within a limited budget so that we do not have to spend more budget on some nodes adjacent to the chosen nodes; our problem is the…

Data Structures and Algorithms · Computer Science 2026-01-30 Sipra Singh

Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…

Data Structures and Algorithms · Computer Science 2025-07-01 Jakub Balabán , Daniel Mock , Peter Rossmanith

A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…

Data Structures and Algorithms · Computer Science 2017-11-22 Robert Bredereck , Piotr Faliszewski , Rolf Niedermeier , Piotr Skowron , Nimrod Talmon

We initiate the study of the parameterized complexity of the {\sc Collective Graph Exploration} ({\sc CGE}) problem. In {\sc CGE}, the input consists of an undirected connected graph $G$ and a collection of $k$ robots, initially placed at…

Data Structures and Algorithms · Computer Science 2023-10-10 Siddharth Gupta , Guy Sa'ar , Meirav Zehavi

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

Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…

Computational Complexity · Computer Science 2018-07-11 Max Bannach , Till Tantau

By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…

Logic in Computer Science · Computer Science 2023-10-03 Max Bannach , Florian Chudigiewitsch , Till Tantau

What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically. As lossless state compression…

Robotics · Computer Science 2024-10-15 Yulin Zhang , Dylan A. Shell

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…

Data Structures and Algorithms · Computer Science 2025-07-01 Manuel Lafond , Bertrand Marchand

Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time $f(k)n^{O(1)}$ and space $f(k)\log(n)$ (for some computable function f). We give a wide variety of…

Computational Complexity · Computer Science 2023-10-24 Hans L. Bodlaender , Carla Groenland , Jesper Nederlof , Céline M. F. Swennenhuis

We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned…

Programming Languages · Computer Science 2008-12-18 Krishnendu Chatterjee , Luca de Alfaro , Rupak Majumdar

Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a \emph{fair} version of \textsc{Hitting Set}. In the…

Data Structures and Algorithms · Computer Science 2023-07-19 Tanmay Inamdar , Lawqueen Kanesh , Madhumita Kundu , Nidhi Purohit , Saket Saurabh

We consider the problem of optimizing a coverage function under a $\ell$-matchoid of rank $k$. We design fixed-parameter algorithms as well as streaming algorithms to compute an exact solution. Unlike previous work that presumes linear…

Data Structures and Algorithms · Computer Science 2022-12-14 Chien-Chung Huang , Justin Ward

We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…

Discrete Mathematics · Computer Science 2023-09-22 Hans L. Bodlaender , Carla Groenland , Michał Pilipczuk

The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…

Computational Geometry · Computer Science 2026-05-07 Éric Colin de Verdière , Petr Hliněný

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

The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code…

Computational Complexity · Computer Science 2018-03-28 Arnab Bhattacharyya , Suprovat Ghoshal , Karthik C. S. , Pasin Manurangsi

A secure set $S$ in a graph is defined as a set of vertices such that for any $X\subseteq S$ the majority of vertices in the neighborhood of $X$ belongs to $S$. It is known that deciding whether a set $S$ is secure in a graph is…

Computational Complexity · Computer Science 2017-07-11 Bernhard Bliem , Stefan Woltran

We show that the dominating set problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K(1,3)), the complete bipartite graph on four vertices where the two parts have one and three…

Data Structures and Algorithms · Computer Science 2015-03-17 Marek Cygan , Geevarghese Philip , Marcin Pilipczuk , Michał Pilipczuk , Jakub Onufry Wojtaszczyk

In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…

Quantum Physics · Physics 2024-08-08 Tatsuya Terao , Ryuhei Mori