Partitioning Harary graphs into connected subgraphs containing prescribed vertices

International audienceA graph G is arbitrarily partitionable (AP for short) if for every partition (n_1, n_2, ..., n_p) of |V(G)| there exists a partition (V_1, V_2, ..., V_p) of V(G) such that each V_i induces a connected subgraph of G with order n_i. If, additionally, k of these subgraphs (k = 1 and n >= k

Further Evidence Towards the Multiplicative 1-2-3 Conjecture

The product version of the 1-2-3 Conjecture, introduced by Skowronek-Kazi{\'o}w in 2012, states that, a few obvious exceptions apart, all graphs can be 3-edge-labelled so that no two adjacent vertices get incident to the same product of labels. To date, this conjecture was mainly verified for complete graphs and 3-colourable graphs. As a strong support to the conjecture, it was also proved that all graphs admit such 4-labellings. In this work, we investigate how a recent proof of the multiset version of the 1-2-3 Conjecture by Vu{\v c}kovi{\'c} can be adapted to prove results on the product version. We prove that 4-chromatic graphs verify the product version of the 1-2-3 Conjecture. We also prove that for all graphs we can design 3-labellings that almost have the desired property. This leads to a new problem, that we solve for some graph classes

Easily rendering token-ring algorithms of distributed and parallel applications fault tolerant

International audienceWe propose in this paper a new algorithm that, when called by existing token ring-based algorithms of parallel and distributed applications, easily renders the token tolerant to losses in presence of node crashes. At most k consecutive node crashes are tolerated in the ring. Our algorithm scales very well since a node monitors the liveness of at most k other nodes and neither a global election algorithm nor broadcast primitives are used to regenerate a new token. It is thus very effective in terms of latency cost. Finally, a study of the probability of having at most k consecutive node crashes in the presence of f failures and a discussion of how to extend our algorithm to other logical topologies are also presented

Gestion dynamique du cache entre machines virtuelles

National audiencePUMA est un mécanisme de cache réparti intégré au noyau Linux qui permet de mutualiser la mémoire inutilisée de machines virtuelles (MVs) pour améliorer les performances des applications intensives en entrées/sorties (E/S). Dans le design initial que nous avons proposé, la configuration de PUMA était essentiellement statique, la quantité de mémoire prêtée par un noeud était difficilement modifiable en cas de variation de charge sur l'un des noeud. Dans cet article, nous proposons plusieurs mécanismes permettant à PUMA d'ajuster dynamiquement la quantité de mémoire prêtée aux MVs en fonction des besoins. Nos évaluations, reposant sur des lectures aléatoires et des allocations de mémoire, montrent que PUMA est capable d'ajuster son activité et la quantité de mémoire prêtée à d'autres noeuds pour éviter de dégrader les performances. Comparé à une approche à de type ballooning automatique, PUMA est capable de récupérer 10 fois plus rapidement la mémoire allouée

From light edges to strong edge-colouring of 1-planar graphs

International audienceA strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$. A conjecture of Erd\H{o}s and Ne\v{s}et\v{r}il, stated back in the $80$'s, asserts that every graph with maximum degree $\Delta$ should have strong chromatic index at most roughly $1.25 \Delta^2$. Several works in the last decades have confirmed this conjecture for various graph classes. In particular, lots of attention have been dedicated to planar graphs, for which the strong chromatic index decreases to roughly $4\Delta$, and even to smaller values under additional structural requirements.In this work, we initiate the study of the strong chromatic index of $1$-planar graphs, which are those graphs that can be drawn on the plane in such a way that every edge is crossed at most once. We provide constructions of $1$-planar graphs with maximum degree~$\Delta$ and strong chromatic index roughly $6\Delta$. As an upper bound, we prove that the strong chromatic index of a $1$-planar graph with maximum degree $\Delta$ is at most roughly $24\Delta$ (thus linear in $\Delta$). The proof of this result is based on the existence of light edges in $1$-planar graphs with minimum degree at least~$3$

Pushable chromatic number of graphs with degree constraints

Pushable homomorphisms and the pushable chromatic number $\chi_p$ of oriented graphs were introduced by Klostermeyer and MacGillivray in 2004. They notably observed that, for any oriented graph $\overrightarrow{G}$, we have $\chi_p(\overrightarrow{G}) \leq \chi_o(\overrightarrow{G}) \leq 2 \chi_p(\overrightarrow{G})$, where $\chi_o(\overrightarrow{G})$ denotes the oriented chromatic number of $\overrightarrow{G}$. This stands as first general bounds on $\chi_p$. This parameter was further studied in later works.This work is dedicated to the pushable chromatic number of oriented graphs fulfilling particular degree conditions. For all $\Delta \geq 29$, we first prove that the maximum value of the pushable chromatic number of an oriented graph with maximum degree $\Delta$ lies between $2^{\frac{\Delta}{2}-1}$ and $(\Delta-3) \cdot (\Delta-1) \cdot 2^{\Delta-1} + 2$ which implies an improved bound on the oriented chromatic number of the same family of graphs. For subcubic oriented graphs, that is, when $\Delta \leq 3$, we then prove that the maximum value of the pushable chromatic number is~$6$ or~$7$. We also prove that the maximum value of the pushable chromatic number of oriented graphs with maximum average degree less than~$3$ lies between~$5$ and~$6$. The former upper bound of~$7$ also holds as an upper bound on the pushable chromatic number of planar oriented graphs with girth at least~$6$

Puma: pooling unused memory in virtual machines for I/O intensive applications

International audienceWith the advent of cloud architectures, virtualization has become a key mechanism. In clouds, virtual machines (VMs) offer both isolation and flexibility. This is the foundation of cloud elasticity, but it induces fragmentation of the physical resources, including memory. While each VM memory needs evolve during time, existing mechanisms used to dynamically adjust VMs memory are inefficient, and it is currently impossible to take benefit of the unused memory of VMs hosted by another host. In this paper we propose Puma, a mechanism that improves I/O intensive applications performance by providing the ability for a VM to entrust clean page-cache pages to other VMs having unsused memory. By reusing the existing page-cache data structures, Puma is very efficient to reclaim the memory lent to another VM. By being distributed, Puma increases the memory consolidation at the scale of a data center. In our evaluations made with TPC-C, TPC-H, BLAST and Postmark, we show that Puma can significantly boost the performance without impacting potential activity peaks on the lender