Related papers: Enumeration and updates for conjunctive linear alg…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
We investigate the enumeration of query results for an important subset of CQs with projections, namely star and path queries. The task is to design data structures and algorithms that allow for efficient enumeration with delay guarantees…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…
We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show…
We study the enumeration of answers to ontology-mediated queries (OMQs) where the ontology is a set of guarded TGDs or formulated in the description logic ELI and the query is a conjunctive query (CQ). In addition to the traditional notion…
Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big…
We propose an algebraic framework for studying efficient algorithms for query evaluation, aggregation, enumeration, and maintenance under updates, on sparse databases. Our framework allows to treat those problems in a unified way, by…
We show that the matrix query language $\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation…
We study the enumeration of answers to ontology-mediated queries when the ontology is formulated in a description logic that supports functional roles and the query is a CQ. In particular, we show that enumeration is possible with linear…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
This paper aims at providing extremely efficient algorithms for approximate query enumeration on sparse databases, that come with performance and accuracy guarantees. We introduce a new model for approximate query enumeration on classes of…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We study the problem of answering conjunctive queries with free access patterns (CQAPs) under updates. A free access pattern is a partition of the free variables of the query into input and output. The query returns tuples over the output…
Even though query evaluation is a fundamental task in databases, known classifications of conjunctive queries by their fine-grained complexity only apply to queries without self-joins. We study how self-joins affect enumeration complexity,…
Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
Marx (STOC~2010, J.~ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class $\Phi$ of Boolean CQs of bounded submodular width, the model-checking problem for $\Phi$ on the class of all…
Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…
In this paper we look at a connection between the $\ell_q,0\leq q\leq 1$, optimization and under-determined linear systems of equations with sparse solutions. The case $q=1$, or in other words $\ell_1$ optimization and its a connection with…
We aim to reason about the correctness of behaviour-preserving transformations of Erlang programs. Behaviour preservation is characterised by semantic equivalence. Based upon our existing formal semantics for Core Erlang, we investigate…