arXiv subjects
Publications and source records attributed to Benoît Groz.
We propose KG-ER, a conceptual schema language for knowledge graphs that describes the structure of knowledge graphs independently of their representation (relational databases, property graphs, RDF) while helping to capture the semantics of the information stored in a knowledge graph.
We consider database schemas consisting of a single binary relation, with key constraints and inclusion dependencies. Over this space of 20 schemas, we completely characterize when one schema is generically dominated by another schema. Generic dominance, a classical notion for measuring information capacity, expresses that every instance of a schema can be uniquely represented in the dominating schema, through application of a deterministic, generic data transformation. Our investigation is motivated both by current interest in schema design for graph databases, as well as by intrinsic scientific interest. We also consider the ternary case, but without inclusion dependencies, and discuss how the notions change in the presence of object identifiers.
We study the cutwidth measure on graphs and ways to bound the cutwidth of a graph by partitioning its vertices. We consider bounds expressed as a function of two quantities: on the one hand, the maximal cutwidth y of the subgraphs induced by the classes of the partition, and on the other hand, the cutwidth x of the quotient multigraph obtained by merging each class to a single vertex. We consider in particular the decomposition of directed graphs into strongly connected components (SCCs): in this case, y is the maximal cutwidth of an SCC, and x is the cutwidth of the directed acyclic condensation multigraph. We show that the cutwidth of a graph is always in O(x + y), specifically it can be upper bounded by 1.5x + y. We also show a lower bound justifying that the constant 1.5 cannot be improved in general
We study the problem of finding, in a directed graph, an st-walk of length r mod q which is edge-minimum, i.e., uses the smallest number of distinct edges. Despite the vast literature on paths and cycles with modularity constraints, to the best of our knowledge we are the first to study this problem. Our main result is a polynomial-time algorithm that solves this task when r and q are constants. We also show how our proof technique gives an algorithm to solve a generalization of the well-known Directed Steiner Network problem, in which connections between endpoint pairs are required to satisfy modularity constraints on their length. Our algorithm is polynomial when the number of endpoint pairs and the modularity constraints on the pairs are constants.
We consider the problem of constructing a Shape Expression Schema (ShEx) that describes the structure of a given input RDF graph. We employ the framework of grammatical inference, where the objective is to find an inference algorithm that is both sound i.e., always producing a schema that validates the input RDF graph, and complete i.e., able to produce any schema, within a given class of schemas, provided that a sufficiently informative input graph is presented. We study the case where the input graph is typed i.e., every node is given with its types. We limit our attention to a practical fragment ShEx0 of Shape Expressions Schemas that has an equivalent graphical representation in the form of shape graphs. We investigate the problem of constructing a canonical representative of a given shape graph. Finally, we present a sound and complete algorithm for shape graphs thus showing that ShEx0 is learnable from typed graphs.
Given a set of $n$ points in a $d$-dimensional space, we seek to compute the skyline, i.e., those points that are not strictly dominated by any other point, using few comparisons between elements. We adopt the noisy comparison model [FRPU94] where comparisons fail with constant probability and confidence can be increased through independent repetitions of a comparison. In this model motivated by Crowdsourcing applications, Groz & Milo [GM15] show three bounds on the query complexity for the skyline problem. We improve significantly on that state of the art and provide two output-sensitive algorithms computing the skyline with respective query complexity $O(nd\log (dk/δ))$ and $O(ndk\log (k/δ))$ where $k$ is the size of the skyline and $δ$ the expected probability that our algorithm fails to return the correct answer. These results are tight for low dimensions.