International audience

Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing algorithms use this to accelerate their execution and to bound their time complexity. Yet, only basic orderings have been tested. In this paper, we show that studying the precise cost of algorithms instead of their bounded complexity leads to faster solutions. We introduce cost functions that link ordering properties with the running time of a given algorithm. We prove that their minimization is NP-hard and propose heuristics to obtain new orderings with different trade-offs between cost reduction and ordering time. Using datasets with up to two billion edges, we show that our heuristics accelerate the listing of triangles by an average of 38% when the ordering is already given as an input, and 16% when the ordering time is included.

A short version will be presented at the conference FSTTCS 2022

We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and is more expressive than the extraction grammars recently introduced by Peterfreund. We study the enumeration problem for annotated grammars: fixing a grammar, and given a string as input, enumerate all annotations of the string that form a word derivable from the grammar. Our first result is an algorithm for unambiguous annotated grammars, which preprocesses the input string in cubic time and enumerates all annotations with output-linear delay. This improves over Peterfreund's result, which needs quintic time preprocessing to achieve this delay bound. We then study how we can reduce the preprocessing time while keeping the same delay bound, by making additional assumptions on the grammar. Specifically, we present a class of grammars which only have one derivation shape for all outputs, for which we can enumerate with quadratic time preprocessing. We also give classes that generalize regular spanners for which linear time preprocessing suffices.

We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We consider this problem on the unit cost RAM model with logarithmic word length, where the problem always has a solution in O(log|w| / log log|w|) per operation. We show that the problem is in O(log log|w|) for languages in an algebraically-defined, decidable class QSG, and that it is in O(1) for another such class QLZG. We show that languages not in QSG admit a reduction from the prefix problem for a cyclic group, so that they require Ω(log|w| /log log|w|) operations in the worst case; and that QSG languages not in QLZG admit a reduction from the prefix problem for the multiplicative monoid U₁ = {0, 1}, which we conjecture cannot be maintained in O(1). This yields a conditional trichotomy. We also investigate intermediate cases between O(1) and O(log log|w|). Our results are shown via the dynamic word problem for monoids and semigroups, for which we also give a classification. We thus solve open problems of the paper of Skovbjerg Frandsen, Miltersen, and Skyum [Skovbjerg Frandsen et al., 1997] on the dynamic word problem, and additionally cover regular languages.

In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query one by one and without repetitions. This enumeration scheme is typically useful when the solutions are treated on the fly or when we want to stop the enumeration once the pertinent solutions have been found. However, with the current schemes, there is no restriction on the order how the solutions are given and this order usually depends on the techniques used and not on the relevance for the user. In this paper we study the enumeration of monadic second order logic (MSO) over words when the solutions are ranked. We present a framework based on MSO cost functions that allows to express MSO formulae on words with a cost associated with each solution. We then demonstrate the generality of our framework which subsumes, for instance, document spanners and adds ranking to them. The main technical result of the paper is an algorithm for enumerating all the solutions of formulae in increasing order of cost efficiently, namely, with a linear preprocessing phase and logarithmic delay between solutions. The novelty of this algorithm is based on using functional data structures, in particular, by extending functional Brodal queues to suit with the ranked enumeration of MSO on words.

We study the design of data publishing mechanisms that allow a collection of autonomous distributed datasources to collaborate to support queries. A common mechanism for data publishing is via views: functions that expose derived data to users, usually specified as declarative queries. Our autonomy assumption is that the views must be on individual sources, but with the intention of supporting integrated queries. In deciding what data to expose to users, two considerations must be balanced. The views must be sufficiently expressive to support queries that users want to ask -- the utility of the publishing mechanism. But there may also be some expressiveness restriction. Here we consider two restrictions, a minimal information requirement, saying that the views should reveal as little as possible while supporting the utility query, and a non-disclosure requirement, formalizing the need to prevent external users from computing information that data owners do not want revealed. We investigate the problem of designing views that satisfy both an expressiveness and an inexpressiveness requirement, for views in a restricted declarative language (conjunctive queries), and for arbitrary views.

Graph databases have received a lot of attention as they are particularly useful in many applications such as social networks, life sciences and the semantic web. Various languages have emerged to query graph databases, many of which embed forms of recursion which reveal essential for navigating in graphs. The relational model has benefited from a huge body of research in the last half century and that is why many graph databases rely on techniques of relational query engines. Since its introduction, the relational model has seen various attempts to extend it with recursion and it is now possible to use recursion in several SQL or Datalog based database systems. The optimization of recursive queries remains, however, a challenge. We propose mu-RA, a variation of the Relational Algebra equipped with a fixpoint operator for expressing recursive relational queries. mu-RA can notably express unions of conjunctive regular path queries. Leveraging the fact that this fixpoint operator makes recursive terms more amenable to algebraic transformations, we propose new rewrite rules. These rules makes it possible to generate new query execution plans, that cannot be obtained with previous approaches. We present the syntax and semantics of mu-RA, and the rewriting rules that we specifically devised to tackle the optimization of recursive queries. We report on practical experiments that show that the newly generated plans can provide significant performance improvements for evaluating recursive queries over graphs.

Data integration systems allow users to access data sitting in multiple sources by means of queries over a global schema, related to the sources via mappings. Datasources often contain sensitive information, and thus an analysis is needed to verify that a schema satisfies a privacy policy, given as a set of queries whose answers should not be accessible to users. Such an analysis should take into account not only knowledge that an attacker may have about the mappings, but also what they may know about the semantics of the sources.In this paper, we show that source constraints can have a dramatic impact on disclosure analysis. We study the problem of determining whether a given data integration system discloses a source query to an attacker in the presence of constraints, providing both lower and upper bounds on source-aware disclosure analysis.

SPARQL is the standard language for querying RDF data. There exists a variety of SPARQL query evaluation systems implementing different architectures for the distribution of data and computations. Differences in architectures coupled with specific optimizations, for e.g. preprocessing and indexing, make these systems incomparable from a purely theoretical perspective. This results in many implementations solving the SPARQL query evaluation problem while exhibiting very different behaviors, not all of them being adapted in any context. We provide a new perspective on distributed SPARQL evaluators, based on multi-criteria experimental rankings. Our suggested set of 5 features (namely velocity, immediacy, dynamicity, parsimony, and resiliency) provides a more comprehensive description of the behaviors of distributed evaluators when compared to traditional runtime performance metrics. We show how these features help in more accurately evaluating to which extent a given system is appropriate for a given use case. For this purpose, we systematically benchmarked a panel of 10 state-of-the-art implementations. We ranked them using a reading grid that helps in pinpointing the advantages and limitations of current technologies for the distributed evaluation of SPARQL queries.

This demonstration showcases ProvSQL, an open-source module for the PostgreSQL database management system that adds support for computation of provenance and probabilities of query results. A large range of provenance formalisms are supported, including all those captured by provenance semirings, provenance semirings with monus, as well as where-provenance. Probabilistic query evaluation is made possible through the use of knowledge compilation tools, in addition to standard approaches such as enumeration of possible worlds and Monte-Carlo sampling. ProvSQL supports a large subset of non-aggregate SQL queries.

International audience