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While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established…

Artificial Intelligence · Computer Science 2012-06-18 Johan Kwisthout , Linda C. van der Gaag

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$…

Computational Complexity · Computer Science 2023-05-05 Ryan L. Mann , Luke Mathieson , Catherine Greenhill

We explore the complexity of computing the optimal pebbling number and pebbling number of a graph. We show that deciding whether the optimal pebbling number of G is at most k is NP-complete and deciding whether the pebbling number of G is…

Combinatorics · Mathematics 2007-05-23 K. Milans , B. Clark

The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have,…

Computational Complexity · Computer Science 2013-08-14 Christoph Stockhusen , Till Tantau

We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \ge 2$ and $k \ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the…

Data Structures and Algorithms · Computer Science 2022-05-24 Fabrizio Montecchiani , Giacomo Ortali , Tommaso Piselli , Alessandra Tappini

For the well-known Survivable Network Design Problem (SNDP) we are given an undirected graph $G$ with edge costs, a set $R$ of terminal vertices, and an integer demand $d_{s,t}$ for every terminal pair $s,t\in R$. The task is to compute a…

Data Structures and Algorithms · Computer Science 2022-11-09 Andreas Emil Feldmann , Anish Mukherjee , Erik Jan van Leeuwen

In a minimal binary constraint network, every tuple of a constraint relation can be extended to a solution. The tractability or intractability of computing a solution to such a minimal network was a long standing open question. Dechter…

Artificial Intelligence · Computer Science 2012-07-26 Georg Gottlob

In this paper a classification of Reidemeister moves, which is the most refined, is introduced. In particular, this classification distinguishes some $\Omega_3$-moves that only differ in how the three strands that are involved in the move…

Geometric Topology · Mathematics 2016-09-07 Olof-Petter OEstlund

We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…

Algebraic Topology · Mathematics 2026-05-25 Navnath Daundkar , Ekansh Jauhari

We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…

Numerical Analysis · Mathematics 2014-12-03 Erich Novak , Daniel Rudolf

We consider the following problem: for a given graph $G$ and two integers $k$ and $d$, can we apply a fixed graph operation at most $k$ times in order to reduce a given graph parameter $\pi$ by at least $d$? We show that this problem is…

Combinatorics · Mathematics 2022-10-20 Felicia Lucke , Felix Mann

The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…

Data Structures and Algorithms · Computer Science 2015-03-19 Gregory Gutin , Eun Jung Kim , Arezou Soleimanfallah , Stefan Szeider , Anders Yeo

We investigate the parameterized complexity of several problems formalizing cluster identification in graphs. In other words we ask whether a graph contains a large enough and sufficiently connected subgraph. We study here three relaxations…

Computational Complexity · Computer Science 2023-03-23 Ambroise Baril , Antoine Castillon , Nacim Oijid

We consider parameterised subgraph-counting problems of the following form: given a graph G, how many k-tuples of its vertices have a given property? A number of such problems are known to be #W[1]-complete; here we substantially generalise…

Computational Complexity · Computer Science 2014-09-26 Mark Jerrum , Kitty Meeks

Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…

Computational Complexity · Computer Science 2025-12-01 Michal Čertík , Andreas Emil Feldmann , Jaroslav Nešetřil , Paweł Rzążewski

Neural networks with ReLU activations are a widely used model in machine learning. It is thus important to have a profound understanding of the properties of the functions computed by such networks. Recently, there has been increasing…

Computational Complexity · Computer Science 2026-05-19 Vincent Froese , Moritz Grillo , Christoph Hertrich , Moritz Stargalla

We study the parametrized complexity of fundamental relations between multidimensional subshifts, such as equality, conjugacy, inclusion, and embedding, for subshifts of finite type (SFTs) and effective subshifts. We build on previous work…

Dynamical Systems · Mathematics 2026-02-16 Nicanor Carrasco-Vargas , Benjamin Hellouin de Menibus , Rémi Pallen

A vertex set $U \subseteq V$ of an undirected graph $G=(V,E)$ is a $\textit{resolving set}$ for $G$, if for every two distinct vertices $u,v \in V$ there is a vertex $w \in U$ such that the distances between $u$ and $w$ and the distance…

Computational Complexity · Computer Science 2018-06-28 Duygu Vietz , Stefan Hoffmann , Egon Wanke

We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…

Computational Complexity · Computer Science 2014-01-14 Jiong Guo , Yash Raj Shrestha

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we…

Computational Complexity · Computer Science 2013-10-14 Nicolas Bourgeois , Konrad K. Dabrowski , Marc Demange , Vangelis Th. Paschos