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View article: Specification and Automatic Verification of Computational Reductions
Specification and Automatic Verification of Computational Reductions Open
We are interested in the following validation problem for computational reductions: for algorithmic problems $P$ and $P^\star$, is a given candidate reduction indeed a reduction from $P$ to $P^\star$? Unsurprisingly, this problem is undeci…
View article: Query Maintenance Under Batch Changes with Small-Depth Circuits
Query Maintenance Under Batch Changes with Small-Depth Circuits Open
Which dynamic queries can be maintained efficiently? For constant-size changes, it is known that constant-depth circuits or, equivalently, first-order updates suffice for maintaining many important queries, among them reachability, tree is…
View article: Givens rotations for QR decomposition, SVD and PCA over database joins
Givens rotations for QR decomposition, SVD and PCA over database joins Open
This article introduces FiGaRo , an algorithm for computing the upper-triangular matrix in the QR decomposition of the matrix defined by the natural join over relational data. FiGaRo ’s main novelty is that it pushes the QR decomposition p…
View article: Dynamic Complexity of Regular Languages: Big Changes, Small Work
Dynamic Complexity of Regular Languages: Big Changes, Small Work Open
Whether a changing string is member of a certain regular language can be maintained in the DynFO framework of Patnaik and Immerman: after changing the symbol at one position of the string, a first-order update formula can express - using a…
View article: Givens QR Decomposition over Relational Databases
Givens QR Decomposition over Relational Databases Open
This paper introduces Figaro, an algorithm for computing the upper-triangular matrix in the QR decomposition of the matrix defined by the natural join over a relational database. The QR decomposition lies at the core of many linear algebra…
View article: Givens Rotations for QR Decomposition, SVD and PCA over Database Joins
Givens Rotations for QR Decomposition, SVD and PCA over Database Joins Open
This article introduces Figaro, an algorithm for computing the upper-triangular matrix in the QR decomposition of the matrix defined by the natural join over relational data. Figaro's main novelty is that it pushes the QR decomposition pas…
View article: Practical Relational Calculus Query Evaluation
Practical Relational Calculus Query Evaluation Open
The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management system…
View article: Dynamic Complexity of Parity Exists Queries
Dynamic Complexity of Parity Exists Queries Open
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…
View article: Dynamic complexity of Reachability: How many changes can we handle?
Dynamic complexity of Reachability: How many changes can we handle? Open
In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-order formulas after inserting or deleting single edges. Later, in 2018, this was extended for changes of size $\frac{\log n}{\log \log n}$, wher…
View article: Dynamic Complexity Meets Parameterised Algorithms
Dynamic Complexity Meets Parameterised Algorithms Open
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic co…
View article: Dynamic Complexity Meets Parameterised Algorithms
Dynamic Complexity Meets Parameterised Algorithms Open
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic co…
View article: A Strategy for Dynamic Programs: Start over and Muddle through
A Strategy for Dynamic Programs: Start over and Muddle through Open
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 util…
View article: A Strategy for Dynamic Programs: Start over and Muddle through
A Strategy for Dynamic Programs: Start over and Muddle through Open
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 util…
View article: Reachability and Distances under Multiple Changes
Reachability and Distances under Multiple Changes Open
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 Patn…
View article: Reachability and Distances under Multiple Changes
Reachability and Distances under Multiple Changes Open
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 Patn…
View article: Dynamic Complexity under Definable Changes
Dynamic Complexity under Definable Changes Open
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 main…
View article: Dynamic Complexity under Definable Changes
Dynamic Complexity under Definable Changes Open
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) AC1 queries can be maintai…
View article: A Strategy for Dynamic Programs: Start over and Muddle Through
A Strategy for Dynamic Programs: Start over and Muddle Through Open
A strategy for constructing dynamic programs is introduced that utilises periodic computation of auxiliary data from scratch and the ability to maintain a query for a limited number of change steps. It is established that if some program c…