Balanced Allocations and Double Hashing

Double hashing has recently found more common usage in schemes that use multiple hash functions. In double hashing, for an item $x$, one generates two hash values $f(x)$ and $g(x)$, and then uses combinations $(f(x) +k g(x)) \bmod n$ for $k=0,1,2,...$ to generate multiple hash values from the initial two. We first perform an empirical study showing that, surprisingly, the performance difference between double hashing and fully random hashing appears negligible in the standard balanced allocation paradigm, where each item is placed in the least loaded of $d$ choices, as well as several related variants. We then provide theoretical results that explain the behavior of double hashing in this context.Comment: Further updated, small improvements/typos fixe

Dynamical system representation of open address hash functions

This paper demonstrates how a broad collection of hash function families can be expressed as dynamical systems. We then show that this representation can be useful for analysis. In particular, we provide an analysis which proves that a widely-used family of double hash functions will transform any initial distribution of keys into the uniform distribution over the table space

Paper Session I-A - Modeling Current and Future Launch Vehicle Processing Using Object-Oriented Simulation Techniques

STARSIM, an acronym for Space Transportation Activities and Resources Simulation, is an objectoriented, menu-driven, user-friendly, decision support system for simulating National Space Transportation System (NSTS) processing, as well as Personnel Launch System (PLS)-National Launch System (NLS), PLS-Proton, PLS-Titan IV, Hermes-Ariane 5 and Cargo Transfer Return Vehicle (CTRV) processing. For each launch system modeled, output is displayed numerically (for global statistical information), in pie chart form (to visualize percentages of subcategories associated with a main category) and in Gantt chart form (for visualizing when and where each launch vehicle experiences waiting, processing, blocking and maintenance periods, and the reasons for blocking). Users may input a comprehensive set of system parameters (e.g., number of launch vehicles, processing times at each facility, number of bays at a particular facility) using a window-based environment, or by supplying an existing input data file. Data for existing launch systems and representative data for proposed systems are used to illustrate output for the models mentioned above. The object-oriented methodology employed in the initial model (i.e., NSTS processing) permitted additional models to be implemented in a minimum amount of time and effort

Open Ocean: Status and Trends, Summary for Policy Makers

The Open Ocean Assessment provides a baseline review of issues linking human well-being with the status of the open ocean through the themes of governance, climate change, ocean ecosystems, fisheries, pollution, and integrated assessment of the human-ocean nexus. It uses indices and indicators where data exist, in many cases with future projections due to global climate change, complemented by expert scientific assessment of numerous low certainty but potentially high impact issues where global ocean monitoring is inadequate

Water

Meta-analysis can be a powerful tool for demonstrating the applicability of a concept beyond the context of individual clinical trials and observational studies, including exploration of effects across different subgroups. Meta-analysis avoids Simpson's paradox, in which a consistent effect in constituent trials is reversed when results are simply pooled. Meta-analysis in critical care medicine is made more complicated, however, by the heterogeneous nature of critically ill patients and the contexts within which they are treated. Failure to properly adjust for this heterogeneity risks missing important subgroup effects in, for example, the interaction of treatment with varying levels of baseline risk. When subgroups are defined by characteristics that vary within constituent trials (such as age) rather than features constant within each trial (such as drug dose), there is the additional risk of incorrect conclusions due to the ecological fallacy. The present review explains these problems and the strategies by which they are overcome