Maximal cliques structure for cocomparability graphs and applications

Il s'agit d'une recherche sur les relations entre les graphes d'intervalles et les graphes de cocomparabilitéA cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and cocomparabil-ity graphs. This study is motivated by recent results [5, 13] that show that for some problems, the algorithm used on interval graphs can also be used with small modifications on cocomparability graphs. Many of these algorithms are based on graph searches that preserve cocomparability orderings. First we propose a characterization of cocomparability graphs via a lattice structure on the set of their maximal cliques. Using this characterization we can prove that every maximal interval subgraph of a cocomparability graph G is also a maximal chordal subgraph of G. Although the size of this lattice of maximal cliques can be exponential in the size of the graph, it can be used as a framework to design and prove algorithms on cocomparability graphs. In particular we show that a new graph search, namely Local Maximal Neighborhood Search (LocalMNS) leads to an O(n + mlogn) time algorithm to find a maximal interval subgraph of a cocomparability graph. Similarly we propose a linear time algorithm to compute all simplicial vertices in a cocomparability graph. In both cases we improve on the current state of knowledge

Reasoning on Feature Models: Compilation-Based vs. Direct Approaches

Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of the FM have been well resolved by translating the FM into a conjunctive normal form (CNF) formula, and then feeding the CNF to a SAT solver. However, this approach has some limits for other important reasoning issues about the FM, such as counting or enumerating configurations. Two mainstream approaches have been investigated in this direction: (i) direct approaches, using tools based on the CNF representation of the FM at hand, or (ii) compilation-based approaches, where the CNF representation of the FM has first been translated into another representation for which the reasoning queries are easier to address. Our contribution is twofold. First, we evaluate how both approaches compare when dealing with common reasoning operations on FM, namely counting configurations, pointing out one or several configurations, sampling configurations, and finding optimal configurations regarding a utility function. Our experimental results show that the compilation-based is efficient enough to possibly compete with the direct approaches and that the cost of translation (i.e., the compilation time) can be balanced when addressing sufficiently many complex reasoning operations on large configuration spaces. Second, we provide a Java-based automated reasoner that supports these operations for both approaches, thus eliminating the burden of selecting the appropriate tool and approach depending on the operation one wants to perform

Semi Automatic Construction of ShEx and SHACL Schemas

We present a method for the construction of SHACL or ShEx constraints for an existing RDF dataset. It has two components that are used conjointly: an algorithm for automatic schema construction, and an interactive workflow for editing the schema. The schema construction algorithm takes as input sets of sample nodes and constructs a shape constraint for every sample set. It can be parametrized by a schema pattern that defines structural requirements for the schema to be constructed. Schema patterns are also used to feed the algorithm with relevant information about the dataset coming from a domain expert or from some ontology. The interactive workflow provides useful information about the dataset, shows validation results w.r.t. the schema under construction, and offers schema editing operations that combined with the schema construction algorithm allow to build a complex ShEx or SHACL schema

Shape Designer for ShEx and SHACL Constraints

International audienceWe present Shape Designer, a graphical tool for building SHACL or ShEx constraints for an existing RDF dataset. Shape Designer allows to automatically extract complex constraints that are satisfied by the data. Its integrated shape editor and validator allow expert users to combine and modify these constraints in order to build an arbitrarily complex ShEx or SHACL schema

Parcours de graphes et applications aux graphes de cocomparabilité

This thesis contains a global study on graph searches, introducing a new formal madel to study graph search.But also we study the applications of known graph searches such as LBFS (Lexicographic Breadth First Search), LDFS (Lexicographic Depth First Search) on cocomparability graphs. To this aim we mainly study the maximal antichain lattice of a partial order.Two new graph searches LexUP and LexDown are proposed and their first properties studied.Cette thèse propose un modèle général de parcours de graphe à base de tie-break sur des ensembles d'étiquettes.Par ailleurs nous étudions la structure des graphes de cocomparabilité (graphes dont les complémentaires sont ordonnables transitivement). En particulier nous les caractérisons à l'aide de la théorie des treillis des antichaînes maximales. Nous montrons commnt calculer simplement à l'iade de parcours de graphes certaines propriétés des graphes de cocomparabilité.Enfin nous proposons deux nouveaux parcours lexicographiques de graphes LEXUP, LEXDOWN dont nous établissons les premières propriétés

A new LBFS-based algorithm for cocomparability graph recognition

International audienc

On the power of graph searching for cocomparability graphs

International audienceIn this paper we study how graph searching on a cocomparability graph G can be used to pro- duce cocomp orderings, (i.e., orderings that are linear extensions of some transitive orientation of G) that yield simple algorithms for various intractable problems in general. Such techniques have been used to find a simple certifying algorithm for the minimum path cover problem. In particular we present a characterization of the searches that preserve cocomp orderings when used as a “+ sweep”. This allows us to present a toolbox of different graph searches and a framework to solve various problems on cocomparability graphs. We illustrate these techniques by describing a very simple certifying algorithm for the maximum independent set problem as well as a simple permutation graph recognition algorithm.Keywords: Cocomparability graphs, comparability graphs, partial orders, linear extensions, graph algorithms, classical graph searches, lexicographic depth first search (LDFS), minimum path cover problem, recognition of permutation graphs

Semi Automatic Construction of ShEx and SHACL Schemas

We present a method for the construction of SHACL or ShEx constraints for an existing RDF dataset. It has two components that are used conjointly: an algorithm for automatic schema construction, and an interactive workflow for editing the schema. The schema construction algorithm takes as input sets of sample nodes and constructs a shape constraint for every sample set. It can be parametrized by a schema pattern that defines structural requirements for the schema to be constructed. Schema patterns are also used to feed the algorithm with relevant information about the dataset coming from a domain expert or from some ontology. The interactive workflow provides useful information about the dataset, shows validation results w.r.t. the schema under construction, and offers schema editing operations that combined with the schema construction algorithm allow to build a complex ShEx or SHACL schema

Semi Automatic Construction of ShEx and SHACL Schemas

We present a method for the construction of SHACL or ShEx constraints for an existing RDF dataset. It has two components that are used conjointly: an algorithm for automatic schema construction, and an interactive workflow for editing the schema. The schema construction algorithm takes as input sets of sample nodes and constructs a shape constraint for every sample set. It can be parametrized by a schema pattern that defines structural requirements for the schema to be constructed. Schema patterns are also used to feed the algorithm with relevant information about the dataset coming from a domain expert or from some ontology. The interactive workflow provides useful information about the dataset, shows validation results w.r.t. the schema under construction, and offers schema editing operations that combined with the schema construction algorithm allow to build a complex ShEx or SHACL schema