Programming non-embarrassingly parallel scientific computing applications such as those involving the numerical resolution of system of PDEs using mesh based methods for grid computing environments is a complex and important issue. This work contributes to this goal by proposing some MPI extensions to let programmers deal with the hierarchical nature of the grid infrastructure thanks to a tree ...

Les arbres sont principalement la structure de donnée utilisés pour stocker des données ordonnées et d’après Knuth la plus importante structure non-linéaire intervenant dans l’informatique. Ils sont très utilisés dans tous les domaines, parce que bien adaptés à la représentation naturelle d’information organisée homogène, et d’une grande rapidité et commodité de manipulation. On trouve cette st...

In this paper we present a new parsing algorithm for linear indexed grammars (LIGs) in the same spirit as the one described in (Vijay-Shanker and Weir, 1993) for tree adjoining grammars. For a LIG L and an input string x of length n, we build a non ambiguous context-free grammar whose sentences are all (and exclusively) valid derivation sequences in L which lead to x. We show that this grammar ...

Solving sparse linear systems can lead to processing tree workflows on a platform of processors. In this study, we use the model of malleable tasks motivated in [1, 9] in order to study tree workflow schedules under two contradictory objectives: makespan minimization and memory minization. First, we give a simpler proof of the result of [8] which allows to compute a makespan-optimal schedule fo...

Given a graph G and a spanning subgraph T of G, a backbone k-colouring for (G,T ) is a mapping c : V (G)→ {1, . . . ,k} such that |c(u)− c(v)| ≥ 2 for every edge uv ∈ E(T ) and |c(u)− c(v)| ≥ 1 for every edge uv ∈ E(G) \E(T ). The backbone chromatic number BBC(G,T ) is the smallest integer k such that there exists a backbone k-colouring of (G,T ). In 2007, Broersma et al. [2] conjectured that B...

— Hopf algebra structures on rooted trees are by now a well-studied object, especially in the context of combinatorics. They are essentially characterized by the coproduct map. In this work we define yet another Hopf algebra H by introducing a new coproduct on a (commutative) algebra of rooted forests, considering each tree of the forest (which must contain at least one edge) as a Feyman-like g...