Related papers: Dynamic Complexity Meets Parameterised Algorithms
In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of model checking a fixed monadic second-order formula over evolving subgraphs of a fixed maximal…
Dynamic Complexity (as introduced by Patnaik and Immerman) tries to express how hard it is to update the solution to a problem when the input is changed slightly. It considers the changes required to some stored data structure (possibly a…
This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) $AC^1$ queries can be…
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…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete…
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges (Patnaik and Immerman…
Graph databases in many applications---semantic web, transport or biological networks among others---are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other…
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We investigate the fine-grained complexity of dynamically maintaining the result of fixed self-join free conjunctive queries under single-tuple updates. Prior work shows that free-connex queries can be maintained in update time…
{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
We propose a probabilistic semantic filtering framework in which parameters of a dynamical system are inferred and associated with a closed set of semantic classes in a map. We extend existing methods to a multi-parameter setting using a…
The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free…
Dynamic Complexity was introduced by Immerman and Patnaik PI97 in the nineties and has seen a resurgence of interest with the positive resolution of their conjecture on directed reachability in DynFO DKMSZ18. Since then many natural…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…