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• W2279770918 abstract "In the talk, we shall discuss quality measures for hash functions usedin data structures and algorithms, and survey positive and negativeresults. (This talk is not about cryptographic hash functions.)For the analysis of algorithms involving hash functions, it is oftenconvenient to assume the hash functions used behave fully randomly; insome cases there is no analysis known that avoids this assumption. Inpractice, one needs to get by with weaker hash functions that can begenerated by randomized algorithms. A well-studied range of applications concern realizations of dynamic dictionaries (linearprobing, chained hashing, dynamic perfect hashing, cuckoo hashing andits generalizations) or Bloom filters and their variants.A particularly successful and useful means of classification areCarter and Wegman's universal or k-wise independent classes,introduced in 1977. A natural and widely used approach to analyzingan algorithm involving hash functions is to show that it works if asufficiently strong universal class of hash functions is used, and tosubstitute one of the known constructions of such classes. Thisinvites research into the question of just how much independence inthe hash functions is necessary for an algorithm to work. Some recentanalyses that gave impossibility results constructed rather artificialclasses that would not work; other results pointed out natural, widelyused hash classes that would not work in a particular application.Only recently it was shown that under certain assumptions on someentropy present in the set of keys even 2-wise independent hashclasses will lead to strong randomness properties in the hash values.The negative results show that these results may not be taken asjustification for using weak hash classes indiscriminately, inparticular for key sets with structure.When stronger independence properties are needed for a theoreticalanalysis, one may resort to classic constructions. Only in 2003 itwas found out how full randomness can be simulated using only linearspace overhead (which is optimal). The split-and-share approachcan be used to justify the full randomness assumption in somesituations in which full randomness is needed for the analysis to gothrough, like in many applications involving multiple hash functions(e.g., generalized versions of cuckoo hashing with multiple hashfunctions or larger bucket sizes, load balancing, Bloom filters andvariants, or minimal perfect hash function constructions).For practice, efficiency considerations beyond constant factors areimportant. It is not hard to construct very efficient 2-wiseindependent classes. Using k-wise independent classes for constant kbigger than 3 has become feasible in practice only by newconstructions involving tabulation. This goes together well with thequite new result that linear probing works with 5-independent hashfunctions.Recent developments suggest that the classification of hash functionconstructions by their degree of independence alone may not beadequate in some cases. Thus, one may want to analyze the behavior ofspecific hash classes in specific applications, circumventing theconcept of k-wise independence. Several such results were recentlyachieved concerning hash functions that utilize tabulation. Inparticular if the analysis of the application involves usingrandomness properties in graphs and hypergraphs (generalized cuckoohashing, also in the version with a stash, or load balancing), ahash class combining k-wise independence with tabulation has turnedout to be very powerful." @default.
• W2279770918 created "2016-06-24" @default.
• W2279770918 creator A5067257613 @default.
• W2279770918 date "2012-02-29" @default.
• W2279770918 modified "2023-09-28" @default.
• W2279770918 title "On Randomness in Hash Functions (Invited Talk)." @default.
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• W2279770918 doi "https://doi.org/10.4230/lipics.stacs.2012.25" @default.
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