Sparsity-Certifying Graph Decompositions

We describe a new algorithm, the (k, ℓ)-pebble game with colors, and use it to obtain a characterization of the family of (k, ℓ)-sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs. Special instances of sparse graphs appear in rigidity theory and have received increased attention in recent years. In particular, our colored pebbles generalize and strengthen the previous results of Lee and Streinu [12] and give a new proof of the Tutte-Nash-Williams characterization of arboricity. We also present a new decomposition that certifies sparsity based on the (k, ℓ)-pebble game with colors. Our work also exposes connections between pebble game algorithms and previous sparse graph algorithms by Gabow [5], Gabow and Westermann [6] and Hendrickson [9]

Natural realizations of sparsity matroids

A hypergraph G with n vertices and m hyperedges with d endpoints each is (k,l)-sparse if for all sub-hypergraphs G' on n' vertices and m' edges, m'\le kn'-l. For integers k and l satisfying 0\le l\le dk-1, this is known to be a linearly representable matroidal family. Motivated by problems in rigidity theory, we give a new linear representation theorem for the (k,l)-sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph G.Comment: Corrected some typos from the previous version; to appear in Ars Mathematica Contemporane

Generic rigidity with forced symmetry and sparse colored graphs

We review some recent results in the generic rigidity theory of planar frameworks with forced symmetry, giving a uniform treatment to the topic. We also give new combinatorial characterizations of minimally rigid periodic frameworks with fixed-area fundamental domain and fixed-angle fundamental domain.Comment: 21 pages, 2 figure

Slider-pinning Rigidity: a Maxwell-Laman-type Theorem

We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley's direction networks.Comment: Accepted, to appear in Discrete and Computational Geometr

Algorithms for detecting dependencies and rigid subsystems for CAD

Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then, we focus on identifying the "special positions" of a design in which generically independent constraints become dependent. We present combinatorial algorithms for identifying subgraphs associated to factors of a particular polynomial, whose vanishing indicates a special position and resulting dependency. Further factoring in the Grassmann- Cayley algebra may allow a geometric interpretation giving conditions (e.g., "these two lines being parallel cause a dependency") determining the special position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract based on v1

L'espace documentaire en restructuration (l'évolution des services des bibliothèques universitaires.)

Le catalogue occupe une place privilégiée dans l offre de service des bibliothèques universitaires, pivot de l intermédiation. Depuis 10 ans, il traverse une crise grave, voyant les usagers le délaisser à la faveur des moteurs de recherche généralistes. Le web, plus qu un sérieux concurrent, devance aujourd hui les systèmes d information documentaires, et devient le point d entrée principal pour la recherche d information. Les bibliothèques tentent de structurer un espace documentaire qui soit habité par les usagers, au sein duquel se développe l offre de service, mais celle-ci se présente encore comme une série de silos inertes, sans grande possibilité de navigation, malgré de considérables efforts d ingénierie et des pistes d évolution vers les outils de découverte. La profession, consciente de cette crise profonde, après avoir accusé les remous occasionnés par la dimension disruptive du numérique, cherche des moyens pour adapter et diversifier son offre, fluidifier la diffusion de l information, et se réinvente un rôle d intermédiation en cherchant à tirer profit des nouvelles pratiques des usagers, de leurs nouvelles attentes, et de nouvelles perspectives. Les bibliothèques placent leur espoir dans de nouveaux modèles de données, tentent d y ajouter un niveau d abstraction favorisant les liaisons avec l univers de la connaissance. L évolution vers le web sémantique semble une opportunité à saisir pour valoriser les collections et les rendre exploitables dans un autre contexte, au prix d importants efforts que cette analyse tente de mesurer. Une approche constructiviste fondée sur l observation participante et le recueil de données offre une vision issue de l intérieur de la communauté des bibliothèques sur l évolution des catalogues et des outils d intermédiation, et ouvre des perspectives sur leurs enjeux.The catalog takes up a special position in the supply of services of academic libraries, as a pivot for the intermediary between users and information professionals who carry the responsibility for building up collections. For 10 years, through a serious crisis, they ve been seeing their patrons preferring the general or commercial search engines. The Web is more than a serious competitor today, ahead of the document information systems, and became the main access point for information retrieval. Libraries are trying to structure an information space that is temporarily or permanently inhabited by users, in which the service offering is developed, but it is still presented as a series of silos, with few opportunities of navigation between them despite considerable engineering efforts and a perspective of evolution towards discovery tools. The profession, having become aware of this deep crisis after accusing eddies caused by the breakdown of the digital switch, looking for ways to adapt and diversify its offering, streamlines the dissemination of information, and reinvents its roles, trying to take advantage of new practices of users, new expectations and new prospects. Libraries put their hope in new data models, trying to add a level of abstraction promoting links with the world of knowledge. The evolution towards the Semantic Web seems to be a valuable opportunity to enhance the collections and make them usable in another context, at the expense of significant efforts sized up by this analysis. A constructivist approach based on participant observation and data collection offers a vision of the outcome within the library community on the development of catalogs and intermediation tools, and an outlook on their issues.PARIS-CNAM (751032301) / SudocSudocFranceF