Related papers: State Complexity Characterizations of Parameterize…
A parameterised Boolean equation system (PBES) is a set of equations that defines sets satisfying the equations as the least and/or greatest fixed-points. Thus this system is regarded as a declarative program defining predicates, where a…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
A well-studied continuous model of graphs considers each edge as a continuous unit-length interval of points. In the problem $\delta$-Tour defined within this model, the objective to find a shortest tour that comes within a distance of…
In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
The \emph{linear vertex arboricity} of a graph is the smallest number of sets into which the vertices of a graph can be partitioned so that each of these sets induces a linear forest. Chaplick et al. [JoCG 2020] showed that, somewhat…
Automata networks can be seen as bare finite dynamical systems, but their growing theory has shown the importance of the underlying communication graph of such networks. This paper tackles the question of what dynamics can be realized up to…
One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This…
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…
A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of…
We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to detect realizability…
For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
We study the parameterized complexity of scheduling unit-time jobs on parallel, identical machines under generalized precedence constraints for minimization of the makespan and the sum of completion times. In our setting, each job is…
Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration…
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…
We consider locally checkable labeling LCL problems in the LOCAL model of distributed computing. Since 2016, there has been a substantial body of work examining the possible complexities of LCL problems. For example, it has been established…
Monadic second order logic (MSO2) plays an important role in parameterized complexity due to the Courcelle's theorem. This theorem states that the problem of checking if a given graph has a property specified by a given MSO2 formula can be…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
We study Cayley configuration spaces of a class of 1 degree-of-freedom linkages (graphs with specified edge lengths), obtained by dropping an edge from a tree-decomposable graph. The class includes well-known mechanisms based on the…