Related papers: A parameterized halting problem, $\Delta_0$ truth …
In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing $W[1]$-hardness proofs for these problems, since XNLP-hardness implies $W[t]$-hardness for…
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…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…
Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
In Defective Coloring we are given a graph $G = (V, E)$ and two integers $\chi_d, \Delta^*$ and are asked if we can partition $V$ into $\chi_d$ color classes, so that each class induces a graph of maximum degree $\Delta^*$. We investigate…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
Random systems of curves exhibiting fluctuating features on arbitrarily small scales ($\delta$) are often encountered in critical models. For such systems it is shown that scale-invariant bounds on the probabilities of crossing events imply…
There has been intensive work on the parameterized complexity of the typically NP-hard task to edit undirected graphs into graphs fulfilling certain given vertex degree constraints. In this work, we lift the investigations to the case of…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The…
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
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 completeness results for inference in Bayesian networks with respect to two different parameterizations, namely the number of variables and the topological vertex separation number. For this we introduce the parameterized…
We analyze the topological structure of the Nehari set for a class of functionals depending on a real parameter $\lambda$, and having two degrees of homogeneity. A special attention is paid to the extremal parameter $\lambda^*$, which is…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…