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Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…

Data Structures and Algorithms · Computer Science 2025-02-20 Eduard Eiben , Tomohiro Koana , Magnus Wahlström

A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of…

Data Structures and Algorithms · Computer Science 2007-05-23 G. Gutin , A. Rafiey , S. Szeider , A. Yeo

\textsc{Densest $k$-Subgraph} is the problem to find a vertex subset $S$ of size $k$ such that the number of edges in the subgraph induced by $S$ is maximized. In this paper, we show that \textsc{Densest $k$-Subgraph} is fixed parameter…

Data Structures and Algorithms · Computer Science 2022-07-21 Tesshu Hanaka

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

Given $k$ input graphs $G_1, \dots ,G_k$, where each pair $G_i$, $G_j$ with $i \neq j$ shares the same graph $G$, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks whether there exists a planar drawing for each input graph…

Data Structures and Algorithms · Computer Science 2025-05-01 Simon D. Fink , Matthias Pfretzschner , Ignaz Rutter

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…

Data Structures and Algorithms · Computer Science 2014-04-24 Akanksha Agrawal , Sathish Govindarajan , Neeldhara Misra

Covering all edges of a graph by a small number of vertices, this is the NP-complete Vertex Cover problem. It is among the most fundamental graph-algorithmic problems. Following a recent trend in studying temporal graphs (a sequence of…

Computational Complexity · Computer Science 2020-07-02 Till Fluschnik , Rolf Niedermeier , Valentin Rohm , Philipp Zschoche

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

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

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

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

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

Combinatorics · Mathematics 2014-07-18 Giovanni Felici , Sokol Ndreca , Aldo Procacci , Benedetto Scoppola

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

The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts,…

Data Structures and Algorithms · Computer Science 2025-04-22 Mohsen Dehghankar , Rahul Raychaudhury , Stavros Sintos , Abolfazl Asudeh

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…

Discrete Mathematics · Computer Science 2014-03-31 Yota Otachi , Pascal Schweitzer

We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so…

Data Structures and Algorithms · Computer Science 2026-02-18 Johannes Blaha , Robert Ganian , Katharina Gillig , Jonathan S. Højlev , Simon Wietheger

In the Telephone Broadcast problem we are given a graph $G=(V,E)$ with a designated source vertex $s\in V$. Our goal is to transmit a message, which is initially known only to $s$, to all vertices of the graph by using a process where in…

Data Structures and Algorithms · Computer Science 2025-04-21 Yudai Egami , Tatsuya Gima , Tesshu Hanaka , Yasuaki Kobayashi , Michael Lampis , Valia Mitsou , Edouard Nemery , Yota Otachi , Manolis Vasilakis , Daniel Vaz

In this paper we study fair variants of MSO$_1$ definable problems parameterized by cluster vertex deletion number, i.e., the smallest number of vertices required to be removed from the graph such that what remains is a collection of…

Data Structures and Algorithms · Computer Science 2026-04-28 Tomáš Masařík , Jędrzej Olkowski , Anna Zych-Pawlewicz

A 3-path vertex cover in a graph is a vertex subset $C$ such that every path of three vertices contains at least one vertex from $C$. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at…

Data Structures and Algorithms · Computer Science 2017-08-08 Mingyu Xiao , Shaowei Kou

The graph matching problem aims to discover a latent correspondence between the vertex sets of two observed graphs. This problem has proven to be quite challenging, with few satisfying methods that are computationally tractable and widely…

Computation · Statistics 2018-07-26 Fei Fang , Daniel L. Sussman , Vince Lyzinski