Related papers: Parameterized complexity of reconfiguration of ato…
Programmable arrays of optical traps enable the assembly of configurations of single atoms to perform controlled experiments on quantum many-body systems. Finding the sequence of control operations to transform an arbitrary configuration of…
A graph vertex-subset problem defines which subsets of the vertices of an input graph are feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of the graph. A reconfiguration variant of a vertex-subset…
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…
We propose the redistribution-reconfiguration (red-rec) algorithm to prepare large configurations of atoms using arrays of dynamic optical traps. Red-rec exploits simple heuristics and exact subroutines to solve atom reconfiguration…
We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…
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…
Defect-free atom arrays have emerged as a powerful and versatile platform for quantum sciences and technologies, offering high programmability and promising scalability. The arrays can be prepared by rearranging atoms from a partially…
Defect-free atom arrays are an important precursor for quantum information processing and quantum simulation. Yet, large-scale defect-free atom arrays can be challenging to realize, due to the losses encountered when rearranging…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
Scaling the size of assembled neutral-atom arrays trapped in optical lattices or optical tweezers is an enabling step for a number of applications ranging from quantum simulations to quantum metrology. However, preparation times increase…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
Trapped atoms near nanophotonics form an exciting platform for bottom-up synthesis of strongly interacting quantum matter. The ability to induce tunable long-range atom-atom interactions with photons presents an opportunity to explore…
Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…
The Set Packing problem is, given a collection of sets $\mathcal{S}$ over a ground set $\mathcal{U}$, to find a maximum collection of sets that are pairwise disjoint. The problem is among the most fundamental NP-hard optimization problems…
We study parameterized and approximation algorithms for a variant of Set Cover, where the universe of elements to be covered consists of points in the plane and the sets with which the points should be covered are segments. We call this…
In reconfiguration, we are given two solutions to a graph problem, such as Vertex Cover or Dominating Set, with each solu tion represented by a placement of tokens on vertices of the graph. Our task is to reconfigure one into the other…
New computational strategies, such as molecular docking, are emerging to speed up the drug discovery process. This method predicts the activity of molecules at the binding site of proteins, helping to select the ones that exhibit desirable…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
In this paper we study the problem of finding a small safe set $S$ in a graph $G$, i.e. a non-empty set of vertices such that no connected component of $G[S]$ is adjacent to a larger component in $G - S$. We enhance our understanding of the…