Description du projet
Concevoir des algorithmes capables d’actualiser leurs résultats
Un algorithme est une liste d’instructions qui transforme une entrée donnée en la sortie souhaitée. Ce paradigme a été appliqué avec succès en théorie et en pratique, mais il ne tient pas compte du fait que les données d’entrée peuvent subir des modifications et que l’algorithme doit traiter chaque actualisation aussi vite que possible. L’objectif du projet DynASoAr, financé par l’UE, est de concevoir des algorithmes novateurs pour des scénarios caractérisés par des données d’entrée dynamiques. Le défi pour de tels algorithmes consiste à actualiser efficacement la sortie du calcul après chaque modification des données sans avoir à effectuer un nouveau calcul à partir de zéro.
Objectif
From a procedural viewpoint, an algorithm is a list of instructions that transforms a given input into the desired output. While this paradigm has been successfully applied in theory and practice, it completely neglects the fact that in many scenarios the input is not given to the algorithm in its entirety at the beginning and might undergo changes that the algorithm needs to react to. Formally, such a situation can be modeled as a game between an adversary creating the sequence of updates to the input and an algorithm that tries to process each of these updates as fast as possible. Researchers have studied such dynamic problems with increasing interest in the past years.
However, many state-of-the-art solutions suffer from at least one of the following drawbacks: (1) Many dynamic algorithms are randomized and assume that the sequence of updates is independent of the random choices made by the algorithm. This is not justified in situations where the next update to the input naturally depends on the previous outputs of the algorithm. (2) Many dynamic algorithms achieve amortized running time guarantees where the stated guarantee on processing each update only holds on average and occasionally significantly more time might be needed. This is insufficient for real-time systems requiring hard worst-case guarantees. The goal of this project is to design dynamic algorithms free from these two shortcomings. Formally, this amounts to giving the adversary the following additional powers: (1) adapting its update sequence to the outputs of the algorithm and (2) discarding the algorithm if some update is not processed in time. While isolated results in this direction exist, with some of them obtained by the PI, the unique feature of this project is the systematic study of these stronger adversarial models for otherwise well-studied dynamic problems. Our results will facilitate the use of dynamic algorithms in both real-world applications and in the design of static algorithms.
Champ scientifique
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Programme(s)
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Régime de financement
ERC-STG - Starting GrantInstitution d’accueil
5020 Salzburg
Autriche