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We give new upper and lower bounds for the {\em dynamic} set cover problem. First, we give a $(1+\epsilon) f$-approximation for fully dynamic set cover in $O(f^2\log n /\epsilon^5)$ (amortized) update time, for any $\epsilon > 0$, where $f$…

Data Structures and Algorithms · Computer Science 2019-05-16 Amir Abboud , Raghavendra Addanki , Fabrizio Grandoni , Debmalya Panigrahi , Barna Saha

In the Directed Long Cycle Hitting Set} problem we are given a directed graph $G$, and the task is to find a set $S$ of at most $k$ vertices/arcs such that $G-S$ has no cycle of length longer than $\ell$. We show that the problem can be…

Data Structures and Algorithms · Computer Science 2020-03-12 Alexander Göke , Dániel Marx , Matthias Mnich

We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multi-layered described by a piece-wise inhomogeneous refractive index. The…

Numerical Analysis · Mathematics 2024-02-23 Peter Elbau , Leonidas Mindrinos , Leopold Veselka

Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…

Methodology · Statistics 2016-05-26 Alexander R. Luedtke , Mark J. van der Laan

The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph $G$ and a parameter $k$, one has to decide if there is a set $S$ of at most $k$ vertices such that $G-S$ is acyclic. Assuming the…

Data Structures and Algorithms · Computer Science 2026-01-16 Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…

Formal Languages and Automata Theory · Computer Science 2019-06-13 Étienne André , Benoît Delahaye , Paulin Fournier

This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…

Systems and Control · Computer Science 2021-04-09 Pierre-Jean Meyer , Samuel Coogan , Murat Arcak

We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\eps)$-approximation to the…

Computational Geometry · Computer Science 2011-12-06 Ashwinkumar Badanidiyuru , Robert Kleinberg , Hooyeon Lee

We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of…

Methodology · Statistics 2022-04-26 Bo Zhang , Hanyang Tian , Guangming Pan

An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…

Data Structures and Algorithms · Computer Science 2022-08-29 Ahammed Ullah

We study the parameterized complexity of evaluating Ontology Mediated Queries (OMQs) based on Guarded TGDs (GTGDs) and Unions of Conjunctive Queries (UCQs), in the case where relational symbols have unrestricted arity and where the…

Logic in Computer Science · Computer Science 2021-06-24 Cristina Feier

The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…

Quantum Physics · Physics 2015-06-18 Stefano Longhi

In Clique Cover, given a graph $G$ and an integer $k$, the task is to partition the vertices of $G$ into $k$ cliques. Clique Cover on unit ball graphs has a natural interpretation as a clustering problem, where the objective function is the…

Data Structures and Algorithms · Computer Science 2024-10-07 Tomohiro Koana , Nidhi Purohit , Kirill Simonov

While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…

Computational Complexity · Computer Science 2024-12-02 Shreya Gupta , Boyang Huang , Russell Impagliazzo , Stanley Woo , Christopher Ye

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

Discrete Mathematics · Computer Science 2008-07-23 J. Diaz , D. Mitsche , X. Perez

We show, assuming the (randomized) Gap Exponential Time Hypothesis (Gap-ETH), that the following tasks cannot be done in $T(k) \cdot N^{o(k)}$-time for any function $T$ where $N$ denote the input size: - $\left(1 - \frac{1}{e} +…

Computational Complexity · Computer Science 2019-10-28 Pasin Manurangsi

We investigate the following above-guarantee parameterization of the classical Vertex Cover problem: Given a graph $G$ and $k\in\mathbb{N}$ as input, does $G$ have a vertex cover of size at most $(2LP-MM)+k$? Here $MM$ is the size of a…

Data Structures and Algorithms · Computer Science 2015-09-15 Shivam Garg , Geevarghese Philip

Parametric timed automata (PTAs) extend the concept of timed automata, by allowing timing delays not only specified by concrete values but also by parameters, allowing the analysis of systems with uncertainty regarding timing behaviors. The…

Formal Languages and Automata Theory · Computer Science 2024-10-03 Étienne André , Johan Arcile , Engel Lefaucheux

We consider the embeddability problem of a graph G into a two-dimensional simplicial complex C: Given G and C, decide whether G admits a topological embedding into C. The problem is NP-hard, even in the restricted case where C is…

Computational Geometry · Computer Science 2025-11-13 Éric Colin de Verdière , Thomas Magnard

In the vertex connectivity augmentation problem, we are given an undirected $n$-vertex graph $G$, a set of links $L \subseteq \binom{V(G)}{2} \setminus E(G)$, and integers $\lambda$ and $k$. The task is to insert at most $k$ links from $L$…

Data Structures and Algorithms · Computer Science 2026-05-13 Tuukka Korhonen , Mikkel Thorup