Related papers: Parameterized Complexity of Two-Interval Pattern P…
Let G = (V, E) be a directed acyclic graph with two distinguished vertices s, t and let F be a set of forbidden pairs of vertices. We say that a path in G is safe, if it contains at most one vertex from each pair {u, v} in F. Given G and F,…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \sum_j w_j C_j$ using the three-field notation. For this problem, a…
We consider the problem of finding, for two pairs $(s_1,t_1)$ and $(s_2,t_2)$ of vertices in an undirected graphs, an $(s_1,t_1)$-path $P_1$ and an $(s_2,t_2)$-path $P_2$ such that $P_1$ and $P_2$ share no edges and the length of each $P_i$…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
We study the complexity of randomized computation of integrals depending on a parameter, with integrands from Sobolev spaces. That is, for $r,d_1,d_2\in{\mathbb N}$, $1\le p,q\le \infty$, $D_1= [0,1]^{d_1}$, and $D_2= [0,1]^{d_2}$ we are…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
We study a variant of Min Cost Flow in which the flow needs to be connected. Specifically, in the Connected Flow problem one is given a directed graph $G$, along with a set of demand vertices $D \subseteq V(G)$ with demands $\mathsf{dem}: D…
The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Paths problem, have been considered. Therefore, we investigate the…
The problem DFA-Intersection-Nonemptiness asks if a given number of deterministic automata accept a common word. In general, this problem is PSPACE-complete. Here, we investigate this problem for the subclasses of commutative automata and…
In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…
The classical pattern matching asks for locating all occurrences of one string, called the pattern, in another, called the text, where a string is simply a sequence of characters. Due to the potential practical applications, it is desirable…
In a reconfiguration version of an optimization problem $\mathcal{Q}$ the input is an instance of $\mathcal{Q}$ and two feasible solutions $S$ and $T$. The objective is to determine whether there exists a step-by-step transformation between…
A deterministic sequence of real numbers in the unit interval is called \emph{equidistributed} if its empirical distribution converges to the uniform distribution. Furthermore, the limit distribution of the pair correlation statistics of a…
The NP-hard 2-Club problem is, given an undirected graph G=(V,E) and l\in N, to decide whether there is a vertex set S\subseteq V of size at least l such that the induced subgraph G[S] has diameter at most two. We make progress towards a…
In this paper, we study the parallel and the space complexity of the graph isomorphism problem (\GI{}) for several parameterizations. Let $\mathcal{H}=\{H_1,H_2,\cdots,H_l\}$ be a finite set of graphs where $|V(H_i)|\leq d$ for all $i$ and…
(see paper for full abstract) We show that the Edge-Disjoint Paths problem is W[1]-hard parameterized by the number $k$ of terminal pairs, even when the input graph is a planar directed acyclic graph (DAG). This answers a question of…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…