Strongly universal string hashing is fast

We present fast strongly universal string hashing families: they can process data at a rate of 0.2 CPU cycle per byte. Maybe surprisingly, we find that these families---though they require a large buffer of random numbers---are often faster than popular hash functions with weaker theoretical guarantees. Moreover, conventional wisdom is that hash functions with fewer multiplications are faster. Yet we find that they may fail to be faster due to operation pipelining. We present experimental results on several processors including low-powered processors. Our tests include hash functions designed for processors with the Carry-Less Multiplication (CLMUL) instruction set. We also prove, using accessible proofs, the strong universality of our families.Comment: Software is available at http://code.google.com/p/variablelengthstringhashing/ and https://github.com/lemire/StronglyUniversalStringHashin

Tag-Cloud Drawing: Algorithms for Cloud Visualization

Tag clouds provide an aggregate of tag-usage statistics. They are typically sent as in-line HTML to browsers. However, display mechanisms suited for ordinary text are not ideal for tags, because font sizes may vary widely on a line. As well, the typical layout does not account for relationships that may be known between tags. This paper presents models and algorithms to improve the display of tag clouds that consist of in-line HTML, as well as algorithms that use nested tables to achieve a more general 2-dimensional layout in which tag relationships are considered. The first algorithms leverage prior work in typesetting and rectangle packing, whereas the second group of algorithms leverage prior work in Electronic Design Automation. Experiments show our algorithms can be efficiently implemented and perform well.Comment: To appear in proceedings of Tagging and Metadata for Social Information Organization (WWW 2007

Attribute Value Reordering For Efficient Hybrid OLAP

The normalization of a data cube is the ordering of the attribute values. For large multidimensional arrays where dense and sparse chunks are stored differently, proper normalization can lead to improved storage efficiency. We show that it is NP-hard to compute an optimal normalization even for 1x3 chunks, although we find an exact algorithm for 1x2 chunks. When dimensions are nearly statistically independent, we show that dimension-wise attribute frequency sorting is an optimal normalization and takes time O(d n log(n)) for data cubes of size n^d. When dimensions are not independent, we propose and evaluate several heuristics. The hybrid OLAP (HOLAP) storage mechanism is already 19%-30% more efficient than ROLAP, but normalization can improve it further by 9%-13% for a total gain of 29%-44% over ROLAP

Faster 64-bit universal hashing using carry-less multiplications

Intel and AMD support the Carry-less Multiplication (CLMUL) instruction set in their x64 processors. We use CLMUL to implement an almost universal 64-bit hash family (CLHASH). We compare this new family with what might be the fastest almost universal family on x64 processors (VHASH). We find that CLHASH is at least 60% faster. We also compare CLHASH with a popular hash function designed for speed (Google's CityHash). We find that CLHASH is 40% faster than CityHash on inputs larger than 64 bytes and just as fast otherwise

Analyzing Large Collections of Electronic Text Using OLAP

Computer-assisted reading and analysis of text has various applications in the humanities and social sciences. The increasing size of many electronic text archives has the advantage of a more complete analysis but the disadvantage of taking longer to obtain results. On-Line Analytical Processing is a method used to store and quickly analyze multidimensional data. By storing text analysis information in an OLAP system, a user can obtain solutions to inquiries in a matter of seconds as opposed to minutes, hours, or even days. This analysis is user-driven allowing various users the freedom to pursue their own direction of research