Provable randomized rounding for minimum-similarity diversification.

When searching for information in a data collection, we are often interested not only in finding relevant items, but also in assembling a diverse set, so as to explore different concepts that are present in the data. This problem has been researched extensively. However, finding a set of items with minimal pairwise similarities can be computationally challenging, and most existing works striving for quality guarantees assume that item relatedness is measured by a distance function. Given the widespread use of similarity functions in many domains, we believe this to be an important gap in the literature. In this paper we study the problem of finding a diverse set of items, when item relatedness is measured by a similarity function. We formulate the diversification task using a flexible, broadly applicable minimization objective, consisting of the sum of pairwise similarities of the selected items and a relevance penalty term. To find good solutions we adopt a randomized rounding strategy, which is challenging to analyze because of the cardinality constraint present in our formulation. Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using an independent approach, which is faster, simpler to implement and completely parallelizable. Our analysis relies on a novel bound for the ratio of Poisson-Binomial densities, which is of independent interest and has potential implications for other combinatorial-optimization problems. We leverage this result to design an efficient randomized algorithm that provides a lower-order additive approximation guarantee. We validate our method using several benchmark datasets, and show that it consistently outperforms the greedy approaches that are commonly used in the literature.

Forecasting short-term data center network traffic load with convolutional neural networks.

Efficient resource management in data centers is of central importance to content service providers as 90 percent of the network traffic is expected to go through them in the coming years. In this context we propose the use of convolutional neural networks (CNNs) to forecast short-term changes in the amount of traffic crossing a data center network. This value is an indicator of virtual machine activity and can be utilized to shape the data center infrastructure accordingly. The behaviour of network traffic at the seconds scale is highly chaotic and therefore traditional time-series-analysis approaches such as ARIMA fail to obtain accurate forecasts. We show that our convolutional neural network approach can exploit the non-linear regularities of network traffic, providing significant improvements with respect to the mean absolute and standard deviation of the data, and outperforming ARIMA by an increasingly significant margin as the forecasting granularity is above the 16-second resolution. In order to increase the accuracy of the forecasting model, we exploit the architecture of the CNNs using multiresolution input distributed among separate channels of the first convolutional layer. We validate our approach with an extensive set of experiments using a data set collected at the core network of an Internet Service Provider over a period of 5 months, totalling 70 days of traffic at the one-second resolution.