Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.Comment: 10 pages, 13 figure

Task Runtime Prediction in Scientific Workflows Using an Online Incremental Learning Approach

Many algorithms in workflow scheduling and resource provisioning rely on the performance estimation of tasks to produce a scheduling plan. A profiler that is capable of modeling the execution of tasks and predicting their runtime accurately, therefore, becomes an essential part of any Workflow Management System (WMS). With the emergence of multi-tenant Workflow as a Service (WaaS) platforms that use clouds for deploying scientific workflows, task runtime prediction becomes more challenging because it requires the processing of a significant amount of data in a near real-time scenario while dealing with the performance variability of cloud resources. Hence, relying on methods such as profiling tasks' execution data using basic statistical description (e.g., mean, standard deviation) or batch offline regression techniques to estimate the runtime may not be suitable for such environments. In this paper, we propose an online incremental learning approach to predict the runtime of tasks in scientific workflows in clouds. To improve the performance of the predictions, we harness fine-grained resources monitoring data in the form of time-series records of CPU utilization, memory usage, and I/O activities that are reflecting the unique characteristics of a task's execution. We compare our solution to a state-of-the-art approach that exploits the resources monitoring data based on regression machine learning technique. From our experiments, the proposed strategy improves the performance, in terms of the error, up to 29.89%, compared to the state-of-the-art solutions.Comment: Accepted for presentation at main conference track of 11th IEEE/ACM International Conference on Utility and Cloud Computin