Data types as algorithms
De l'utilisation de la notion de clique (sous-graphe complet symétrique) en matière de typologie de populations
Decomposition of a Symmetric Matrix (Handbook Series Linear Algebra).
Description of the Connected Components of a Semialgebraic Set in Single Exponential Time.
Deux constructions équivalentes d'un jeu d'arrangements pour les fichiers inverses multi-indices
Deux problèmes d'analyse d'algorithmes
Die Berechnungskomplexität von elementarsymmetrischen Funkit
Differential approximation of NP-hard problems with equal size feasible solutions
In this paper, we focus on some specific optimization problems from graph theory, those for which all feasible solutions have an equal size that depends on the instance size. Once having provided a formal definition of this class of problems, we try to extract some of its basic properties; most of these are deduced from the equivalence, under differential approximation, between two versions of a problem which only differ on a linear transformation of their objective functions. This is notably...
Differential approximation of NP-hard problems with equal size feasible solutions
In this paper, we focus on some specific optimization problems from graph theory, those for which all feasible solutions have an equal size that depends on the instance size. Once having provided a formal definition of this class of problems, we try to extract some of its basic properties; most of these are deduced from the equivalence, under differential approximation, between two versions of a problem π which only differ on a linear transformation of their objective functions. This is notably...
Differential equations, Spencer cohomology, and computing resolutions.
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...
Distance entre les racines d'un polynôme
Distributed aggregative optimization with quantized communication
In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking...
Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate
Distributed optimization over unbalanced graphs is an important problem in multi-agent systems. Most of literatures, by introducing some auxiliary variables, utilize the Push-Sum scheme to handle the widespread unbalance graph with row or column stochastic matrix only. But the introduced auxiliary dynamics bring more calculation and communication tasks. In this paper, based on the in-degree and out-degree information of each agent, we propose an innovative distributed optimization algorithm to reduce...
Double-coset enumeration algorithm for symmetrically generated groups.
Dynamic programming for reduced NFAs for approximate string and sequence matching
searching for all occurrences of a pattern (string or sequence) in some text, where the pattern can occur with some limited number of errors given by edit distance. Several methods were designed for the approximate string matching that simulate nondeterministic finite automata (NFA) constructed for this problem. This paper presents reduced NFAs for the approximate string matching usable in case, when we are interested only in occurrences having edit distance less than or equal to a given integer,...