TBA
summary: TBA
TBA
summary: TBA
A simple counting argument applied to lower bounds on the growth of subshifts
summary: Given a group G, a set of colors A and a set of forbidden patterns F, the subshift X_F is the set of colorings of G by A that avoid the patterns in F. I recently obtained a simple condition on the set of forbidden patterns F that implies ...
Boolean dimension of boolean lattices
summary: Partially ordered sets (or posets for short) are structures that arise naturally in mathematics in the study of binary relations between objects. A poset consists of a ground set -- a set of elements -- and a partial order among them, and are usually visualled with directed acyclic graphs (DAGs). Indeed ...
Efficient maximal cliques enumeration in weakly closed graphs
summary: We show that the algorithm presented in [J. Fox, T. Roughgarden, C. Seshadhri, F. Wei, and N. Wein. Finding cliques in social networks: A new distribution-free model. SIAM journal on computing, 49(2):448-464, 2020] can be modified to have enumeration time complexity αO(n·poly(c)). Here parameter ...
Coordonnées explicites pour le s-permutoèdre
En 2019, Viviane Pons et Cesar Ceballos ont introduit une généralisation de l'ordre faible avec un paramètre s qui est un vecteur d'entiers. Ils ont conjecturé (et prouvé en dimensions 2 et 3) que cette structure admettait une réalisation géométrique comme complexe polytopal. En collaboration avec Daniel Tamayo ...
Auction mechanisms for allocation and pricing in Edge Computing
summary: Soon, billions of devices will be connected to the Internet, and most of them will need external resources to store and process their data. Edge Computing can benefit these devices by making these resources available at the network's edges to be closer to the user. However, these offered ...
A Closure Lemma for tough graphs and Hamiltonian degree conditions
summary: A graph G is Hamiltonian if there exists a cycle in G containing all vertices of G exactly once. A graph G is t-tough if, for all subsets of vertices S, the number of connected components in G−S is at most |S|/t. We extended the theorem of ...
Memory-Optimization for Self-Stabilizing Distributed Algorithms
summary: Self-stabilization is a suitable paradigm for distributed systems, particularly prone to transient faults. Errors such as memory or messages corruption, break of a communication link, can put the system in an inconsistent state. A protocol is self-stabilizing if, whatever the initial state of the system, it guarantees that it ...
Algorithmes de partitionnement par comparaison de paires
On cherche à reconstruire une partition d'un ensemble donné en envoyant des paires d'éléments à un oracle qui nous indique s'ils appartiennent à la même partie de la partition. Nous cherchons les algorithmes qui retrouvent la partition en un minimum de questions à l'oracle. Ce problème ...
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