Related papers: Dynamic Complexity of Parity Exists Queries
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely…
Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
An ordered graph is a graph enhanced with a linear order on the vertex set. An ordered graph is a core if it does not have an order-preserving homomorphism to a proper subgraph. We say that $H$ is the core of $G$ if (i) $H$ is a core, (ii)…
In this paper, we study unique colourings in random graphs as a generalization of both conflict-free and injective colourings. Specifically, we impose the condition that a fraction of vertices in the neighbourhood of any vertex are assigned…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the…
For a $k$-uniform hypergraph $F$ let $\textrm{ex}(n,F)$ be the maximum number of edges of a $k$-uniform $n$-vertex hypergraph $H$ which contains no copy of $F$. Determining or estimating $\textrm{ex}(n,F)$ is a classical and central problem…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…
Interval graphs and interval orders are deeply linked. In fact, edges of an interval graphs represent the incomparability relation of an interval order, and in general, of different interval orders. The question about the conditions under…
We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be…
Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…
One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…
We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL's COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query…
Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…
A proper vertex colouring of a graph is \emph{nested} if the vertices of each of its colour classes can be ordered by inclusion of their open neighbourhoods. Through a relation to partially ordered sets, we show that the nested chromatic…
A successor-invariant first-order formula is a formula that has access to an auxiliary successor relation on a structure's universe, but the model relation is independent of the particular interpretation of this relation. It is well known…
Finding the shortest path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has been successfully attempted on this problem, most of which is limited to static graphs.…
We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for $(\Delta+1)$- vertex coloring and…
Order-invariant first-order logic is an extension of first-order logic FO where formulae can make use of a linear order on the structures, under the proviso that they are order-invariant, i.e. that their truth value is the same for all…