A hit rate curve is a function that maps cache size to the proportion of requests that can be served from the cache. (The caching policy and sequence of requests are assumed to be fixed.) Hit rate curves have been studied for decades in the operating system, database and computer architecture communities. They are useful tools for designing appropriate cache sizes, dynamically allocating memory between competing caches, and for summarizing locality properties of the request sequence. In this paper we focus on the widely-used LRU caching policy. Computing hit rate curves is very efficient from a runtime standpoint, but existing algorithms are not efficient in their space usage. For a stream of m requests for n cacheable objects, all existing algorithms that provably compute the hit rate curve use space linear in n. In the context of modern storage systems, n can easily be in the billions or trillions, so the space usage of these algorithms makes them impractical. We present the first algorithm for provably approximating hit rate curves for the LRU policy with sublinear space. Our algorithm uses O( p^2 * log(n) * log^2(m) / epsilon^2 ) bits of space and approximates the hit rate curve at p uniformly-spaced points to within additive error epsilon. This is not far from optimal. Any single-pass algorithm with the same guarantees must use Omega(p^2 + epsilon^{-2} + log(n)) bits of space. Furthermore, our use of additive error is necessary. Any single-pass algorithm achieving multiplicative error requires Omega(n) bits of space.

For an investigative journalist, a large collection of documents obtained from a Freedom of Information Act request or a leak is both a blessing and a curse: such material may contain multiple newsworthy stories, but it can be difficult and time consuming to find relevant documents. Standard text search is useful, but even if the search target is known it may not be possible to formulate an effective query. In addition, summarization is an important non-search task. We present Overview, an application for the systematic analysis of large document collections based on document clustering, visualization, and tagging. This work contributes to the small set of design studies which evaluate a visualization system "in the wild", and we report on six case studies where Overview was voluntarily used by self-initiated journalists to produce published stories. We find that the frequently-used language of "exploring" a document collection is both too vague and too narrow to capture how journalists actually used our application. Our iterative process, including multiple rounds of deployment and observations of real world usage, led to a much more specific characterization of tasks. We analyze and justify the visual encoding and interaction techniques used in Overview's design with respect to our final task abstractions, and propose generalizable lessons for visualization design methodology.

We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel, force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm makes local minima less likely while the GPU parallelism improves speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark datasets. We also show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm.