Related papers: Courcelle's Theorem Made Dynamic
This study introduces a new metric called ''DynamicScore'' to evaluate the dynamics of graphs. It can be applied to both vertices and edges. Unlike traditional metrics, DynamicScore not only measures changes in the number of vertices or…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Algorithmic meta-theorems, stating that graph properties expressible in some particular logic can be decided efficiently in graph classes having some specific structural properties, are now standard in sequential graph algorithms. One of…
We present a dynamic data structure for representing a graph $G$ with tree-depth at most $D$. Tree-depth is an important graph parameter which arose in the study of sparse graph classes. The structure allows addition and removal of edges…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…
The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without…
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been…
Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…
During the last 10 years it has become popular to study dynamic graph problems in a emergency planning or sensitivity setting: Instead of considering the general fully dynamic problem, we only have to process a single batch update of size…
There is a widespread assumption that the universe in general, and the Earth's biosphere in particular, is becoming more complex over time. This paper formulates this assumption as a macroscopic law, the law of increasing complexity, for a…
We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
Bounded treewidth and Monadic Second Order (MSO) logic have proved to be key concepts in establishing fixed-parameter tractability results. Indeed, by Courcelle's Theorem we know: Any property of finite structures, which is expressible by…
Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees $\delta_p(f)$, $1\le p\le {\rm dim}(X)$. We give the definition of the dynamical degrees show how they are…
Dynamic Complexity was introduced by Immerman and Patnaik \cite{PatnaikImmerman97} (see also \cite{DongST95}). It has seen a resurgence of interest in the recent past, see…
Even after the proposal of various solution algorithms, the precise computational complexity of checking whether a Conditional Temporal Network is Dynamically Controllable had still remained widely open. This issue gets settled in this…
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…