Displaying similar documents to “The three-dimensional Gauss algorithm is strongly convergent almost everywhere.”

Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems

Brigitte Vallée (2000)

Journal de théorie des nombres de Bordeaux


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...

Measuring the problem-relevant information in input

Stefan Dobrev, Rastislav Královič, Dana Pardubská (2009)

RAIRO - Theoretical Informatics and Applications


We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of the output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request,...