Marina Moscarini

Distance-hereditary graphs, Steiner trees, and connected domination

Distance-hereditary graphs have been introduced by Howorka and studied in the literature with respect to their metric properties. In this paper several equivalent characterizations of these graphs are given: in terms of existence of particular kinds of vertices (isolated, leaves, twins) and in terms of properties of connections, separators, and hangings. Distance-hereditary graphs are then studied from the algorithmic viewpoint: simple recognition algorithms are given and it is shown that the problems of finding cardinality Steiner trees and connected dominating sets are polynomially solvable in a distance-hereditary graph.

Inclusion and equivalence between relational database schemata

Abstract Conceptual relations among relational database schemata are investigated. Two different definitions of inclusion and a definition of equivalence between schemata are given. Several examples of practical situations adequately handled by our definitions are shown. Finally, necessary and sufficient conditions for inclusion and equivalence are proved for two classes of schemata, meaningful in the relational theory.

Auditing sum-queries to make a statistical database secure

In response to queries asked to a statistical database, the query system should avoid releasing summary statistics that could lead to the disclosure of confidential individual data. Attacks to the security of a statistical database may be direct or indirect and, in order to repel them, the query system should audit queries by controlling the amount of information released by their responses. This paper focuses on sum-queries with a response variable of nonnegative real type and proposes a compact representation of answered sum-queries, called an information model in “normal form,” which allows the query system to decide whether the value of a new sum-query can or cannot be safely answered. If it cannot, then the query system will issue the range of feasible values of the new sum-query consistent with previously answered sum-queries. Both the management of the information model and the answering procedure require solving linear-programming problems and, since standard linear-programming algorithms are not polynomially bounded (despite their good performances in practice), effective procedures that make a parsimonious use of them are stated for the general case. Moreover, in the special case that the information model is “graphical.” It is shown that the answering procedure can be implemented in polynomial time.

On hypergraph acyclicity and graph chordality

Abstract Concepts of acyclicity in hypergraphs and chordality in graphs are related by showing that a hierarchy of well-studied classes of chordal graphs corresponds to the hierarchy of classes of acyclic hypergraphs studied in relational database theory (Fagin, 1983).

Minimal Coverings of Acyclic Database Schemata

In this chapter classes of acyclic hypergraphs associated with classes of relational database schemata are investigated. Various concepts of minimal coverings over a given set of nodes are considered, their interpretation in terms of the relational model is given and their properties studied with respect to the acyclicity degree of the hypergraphs. Several results concerning the computational complexity of determining minimal coverings are provided.

Dynamic query interpretation in relational databases

Abstract A new dynamic approach to the problem of determining the correct interpretation of a logically independent query to a relational database is formally described. A simple kind of conjunctive query is taken into account and the proposed disambiguating process is based on a simple user-system dialogue that consists of a sequence of decisions about the relevance (or not) of an attribute with respect to the user interpretation. A characterization of unambiguous and disambiguable databases is given and properties of such databases are studied. Approximate answers and weaker concepts of unambiguity and disambiguability are also studied. Finally, criteria to select good disambiguation strategies according to the logical independence degree and the naturalness are discussed.

Decomposition of a hypergraph by partial-edge separators

The notion of vertex separability by partial edges for a simple hypergraph is introduced and the related structural properties of the hypergraph are analyzed in terms of maximal (with respect to set-theoretic inclusion) compacts and of dividers, where a compact is a vertex set in which every two vertices are separated by no partial edge, and a divider is a partial edge X for which there exists a pair of vertices that are separated by X and by no proper subset of X. It is proven that, given a hypergraph H, the hypergraph (called the compaction of H) made up of maximal compacts of H is acyclic and coincides with H if and only if H is acyclic; furthermore, it has the same dividers as H, and can be characterized as being the unique acyclic hypergraph that has the same compacts as H. Polynomial algorithms for finding maximal compacts and dividers of a given hypergraph are provided. Finally, an application to the problem of computing the maximum-entropy extension of a system of marginals over a hypergraph is discussed.

Computational issues connected with the protection of sensitive statistics by auditing sum-queries

An implementation of the auditing strategy is presented to avoid both exact and approximate disclosure. The key data structure is a query map, which is a graphical summary of answered queries. Since the size of a query map may be exponential in the number of answered queries, a query-restriction criterion is introduced to make every query map a graph. An auditing procedure on such a graph is presented and the computational issues connected with its implementation are discussed. All the computational tasks can be carried out efficiently but one, which is a provably intractable problem.

Suppressing marginal cells to protect sensitive information in a two-dimensional statistical table (extended abstract)

We propose a method to protect sensitive information in a two-dimensional statistical table based on the suppression of certain marginal cells. A sensitive cell set is considered unprotected if its exact value can be computed from the values of nonsensitive cells and unsuppressed marginal cells. We provide efficient algorithms to solve the following problems: deciding whether the sensitive cell sets are protected, identifying and evaluating all unprotected cell sets, suppressing the fewest marginal cells to protect all the sensitive cells.

A Fast Algorithm for Query Optimization in Universal-Relation Databases

The method of the canonical connection introduced by Maier and Ullman provides an optimal procedure for query processing in universal-relation databases. We present an algorithm for computing canonical connections in a database scheme which is more efficient than the classical algorithm based on tableau reduction. Moreover, with a slight modification of the algorithm we obtain a join plan which succeeds in controlling the nonmonotonicity of cyclic canonical connections.