Comparing slopes is a fundamental graph reading task and the aspect ratio chosen for a plot influences how easy these comparisons are to make. According to Banking to 45°, a classic design guideline first proposed and studied by Cleveland et al., aspect ratios that center slopes around 45° minimize errors in visual judgments of slope ratios. This paper revisits this earlier work. Through exploratory pilot studies that expand Cleveland et al.'s experimental design, we develop an empirical model of slope ratio estimation that fits more extreme slope ratio judgments and two common slope ratio estimation strategies. We then run two experiments to validate our model. In the first, we show that our model fits more generally than the one proposed by Cleveland et al. and we find that, in general, slope ratio errors are not minimized around 45°. In the second experiment, we explore a novel hypothesis raised by our model: that visible baselines can substantially mitigate errors made in slope judgments. We conclude with an application of our model to aspect ratio selection.

The aspect ratio of a plot has a dramatic impact on our ability to perceive trends and patterns in the data. Previous approaches for automatically selecting the aspect ratio have been based on adjusting the orientations or angles of the line segments in the plot. In contrast, we recommend a simple, effective method for selecting the aspect ratio: minimize the arc length of the data curve while keeping the area of the plot constant. The approach is parameterization invariant, robust to a wide range of inputs, preserves visual symmetries in the data, and is a compromise between previously proposed techniques. Further, we demonstrate that it can be effectively used to select the aspect ratio of contour plots. We believe arc length should become the default aspect ratio selection method.

MapReduce is a popular framework for data-intensive distributed computing of batch jobs. To simplify fault tolerance, the output of each MapReduce task and job is materialized to disk before it is consumed. In this demonstration, we describe a modified MapReduce architecture that allows data to be pipelined between operators. This extends the MapReduce programming model beyond batch processing, and can reduce completion times and improve system utilization for batch jobs as well. We demonstrate a modified version of the Hadoop MapReduce framework that supports online aggregation, which allows users to see "early returns" from a job as it is being computed. Our Hadoop Online Prototype (HOP) also supports continuous queries, which enable MapReduce programs to be written for applications such as event monitoring and stream processing. HOP retains the fault tolerance properties of Hadoop, and can run unmodified user-defined MapReduce programs.