Stéphane Grumbach

A new challenge for compression algorithms: genetic sequences

Universal data compression algorithms fail to compress genetic sequences. It is due to the specificity of this particular kind of “text.” We analyze in some detail the properties of the sequences, which cause the failure of classical algorithms. We then present a lossless algorithm, biocompress-2, to compress the information contained in DNA and RNA sequences, based on the detection of regularities, such as the presence of palindromes. The algorithm combines substitutional and statistical methods, and to the best of our knowledge, leads to the highest compression of DNA. The results, although not satisfactory, give insight to the necessary correlation between compression and comprehension of genetic sequences.

Compression of DNA sequences

The authors propose a lossless algorithm based on regularities, such as the presence of palindromes, in the DNA. The results obtained, although not satisfactory, are far beyond classical algorithms.<<ETX>>

COL: A Logic-Based Language for Complex Objects

A logic-based language for manipulating complex objects constructed using set and tuple constructors is introduced. A key feature of the language is the use of base and derived data functions. Under some stratification restrictions, the semantics of programs is given by a canonical minimal and causal model that can be computed using a finite sequence of fixpoints. Applications of the language to procedural data, semantic database models, heterogeneous databases integration, and datalog query evaluation are presented.

The DEDALE system for complex spatial queries

This paper presents DEDALE, a spatial database system intended to overcome some limitations of current systems by providing an abstract and non-specialized data model and query language for the representation and manipulation of spatial objects. DEDALE relies on a logical model based on linear constraints, which generalizes the constraint database model of [KKR90]. While in the classical constraint model, spatial data is always decomposed into its convex components, in DEDALE holes are allowed to fit the need of practical applications. The logical representation of spatial data although slightly more costly in memory, has the advantage of simplifying the algorithms. DEDALE relies on nested relations, in which all sorts of data (thematic, spatial, etc.) are stored in a uniform fashion. This new data model supports declarative query languages, which allow an intuitive and efficient manipulation of spatial objects. Their formal foundation constitutes a basis for practical query optimization. We describe several evaluation rules tailored for geometric data and give the specification of an optimizer module for spatial queries. Except for the latter module, the system has been fully implemented upon the O2 DBMS, thus proving the effectiveness of a constraint-based approach for the design of spatial database systems.

A rule-based language with functions and sets

A logic based language for manipulating complex objects constructed using set and tuple constructors is introduced. A key feature of the COL language is the use of base and derived data functions. Under some stratification restrictions, the semantics of programs is given by a minimal and justified model that can be computed using a finite sequence of fixpoints. The language is extended using external functions and predicates. An implementation of COL in a functional language is briefly discussed.

Spatio-temporal data handling with constraints

Most spatial information systems are limited to a fixed dimension (generally 2) which is not extensible. On the other hand, the emerging paradigm of constraint databases allows the representation of data of arbitrary dimension, together with abstract query languages. The complexity of evaluating queries though might be costly if the dimension of the objects is really arbitrary. In this paper, we present a data model, based on linear constraints, dedicated to the representation and manipulation of multidimensional data. In order to preserve a low complexity for query evaluation, we restrict the orthographic dimension of an object O, defined as the dimension of the components O1 ,..., On such that O=O1×...× On. This allows to process queries independently on each component, therefore achieving a satisfying trade-off between design simplicity, expressive power of the query language and efficiency of query evaluation. We illustrate these concepts in the context of spatio-temporal databases where space and time are the natural components. This data model has been implemented in the DEDALE system and a spatio-temporal application, with orthographic dimension 2, is currently running, thus showing the practical relevance of the approach.

Queries with arithmetical constraints

In this paper, we study the expressive power and the complexity of first-order logic with arithmetic, as a query language over relational and constraint databases. We consider constraints over various domains (N, Z, Q, and R), and with various arithmetical operations (⩽, +, ×, etc.). We first consider the data complexity of first-order queries. We prove in particular that linear queries can be evaluated in AC0 over finite integer databases, and in NC1 over linear constraint databases. This improves previously known bounds. We also show that over all domains, enough arithmetic lead to arithmetical queries, therefore, showing the frontiers of constraints for database purposes. We then tackle the problem of the expressive power, with the definability of the parity and the connectivity, which are the most classical examples of queries not expressible in first-order logic over finite structures. We prove that these two queries are first-order definable in the presence of (enough) arithmetic. Nevertheless, we show that they are not definable with constraints of interest for constraint databases such as linear constraints for instance. Finally, we developed reduction techniques for queries over constraint databases, that allow us to draw conclusions with respect to their undefinability in various constraint query languages.

Towards Tractable Algebras for Bags

Bags, i.e., sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power and increases its complexity. We consider two main issues, namely (i) the impact of the depth of bag nesting on the expressive power and (ii) the complexity and the expressive power induced by the algebraic operations. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator.

Querying aggregate data

1 Introduction We introduce a first-order language with real polynomial arithmetic and aggregation operators (count, iterated sum and multi:ply), which is well suited for the definition of aggregate queries involving complex statistical functions. It offers a good trade-off between expressive power and complexi.ty, with a tractable data complexity. Interestingly, some fundamental properties of first-order with real arithmetic are preserved in the presence of aggregates. In particular, there is an effective quantifier elimination for formulae with aggregation. We consider the problem of querying data that has already been aggregated in aggregate views, and focus on queries with an aggregation over a conjunctive query. Our main conceptual contribution is the introduction of a new equivalence relation among conjunctive queries, the isomorphism modulo a product. We prove that the equivalence of aggregate queries such as for instance averages reduces to it. Deciding if two queries are iso-morphic modulo a product is shown to be NP-complete. We then show that the problem of complete rewriting of count queries using count views is also NP-complete. Finally, we introduce new rewriting techniques based on the isomorphism modulo a product to recover the values of counts by complex arithmetical computation from the views. We conclude by showing how these techniques can be-used to perform automatic aggrega-tion. The manipulation of aggregate data has gained considerable interest in recent years, for its great impact in various applications such as for instance data wareh.ous,-ing. In such applications, queries involve aggregation over evolving data of very large size. The use of ma.-terialized aggregate views, might strongly increase the efficiency of query processing. The modeling and the manipulation of statistical data have been studied with different focus both in the field of statistical databases [Su83, SW85, OOM87, Gho86, RR93, RBT96], and in the field of on-line analytical processing (OLAP) [GBLP96, HRU96, LS97, Sho97]. The real challenge of this sort of data is caused by the rather intricate semantics of summary values, that is not handled by classical database systems. A fundamental problem of statistical databases, is to determine what can be derived from the statistical data. This problem, known as the statistical inference problem is fundamental both for restricting the derivable data for the protection of private data, as well as for deriving new data, by further aggregation of the statistical data, or by automatic aggregation. Permission to make digital or hard copies of all or part of this work for personal …

Finitely Representable Databases

We study infinite but finitely representable databases based on constraints, motivated by new database applications such as those involving spatio-temporal information. We introduce a general definition of finite representation and define the concept of a query as a generalization of a query over relational databases. We investigate the theory of finitely representable models and prove that it differs from both classical model theory and finite model theory. In particular, we show the failure of most of the well-known theorems of logic (compactness, completeness, etc.). An important consequence is that properties such as query satisfiability and containment are undecidable. We illustrate the use of Ehrenfeucht?Frai?sse games on the expressive power of query languages over finitely representable databases. As a case study, we focus on queries over dense order constraint databases. We consider in particular “order-generic” queries which are mappings closed under order-preserving bijections and topological queries, mappings closed under homeomorphisms. We prove that many interesting queries such as topological connectivity are not first-order definable with dense order constraints. We then consider an inflationary fixpoint query language, and prove that it captures exactly all PTIME order-generic queries. Finally, we give a rapid survey of recent results for more general contexts, such as polynomial constraints.