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Closed Hashing is Computable and Optimally Randomizable with Universal Hash Functions
"... Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing, uniform hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1 1\Gammaff +O( 1 n ) for the insertion of the ffnth item into a ta ..."
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Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing, uniform hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1 1\Gammaff +O( 1 n ) for the insertion of the ffnth item into a table of size n, for any fixed ff ! 1. This performance is optimal. These results are derived from a novel formulation that overestimates the expected probe count by underestimating the presence of local items already inserted into the hash table, and from a very sharp analysis of the underlying stochastic structures formed by colliding items. Analogous bounds are attained for the expected rth moment of the probe count, for any fixed r, and linear probing is also shown to achieve a performance with universal hash functions that is equivalent to the fully random case. Categories and Subject Descriptors: E.1 [Data]: Data Structuresarrays; tables; E.2 [Data]: Data Storage Representationsha...
Double Hashing is Computable and Randomizable with Universal Hash Functions
"... Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1/(1alpha) + epsilon for the insertion of the alpha nth item into a table of size n, f ..."
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Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1/(1alpha) + epsilon for the insertion of the alpha nth item into a table of size n, for any fixed alpha 0. This performance is within epsilon of optimal. These results are derived from a novel formulation that overestimates the expected probe count by underestimating the presence of partial items already inserted into the hash table, and from a sharp analysis of the underlying stochastic structures formed by colliding items.
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"... A novel extension to external double hashing providing significant reduction to both successful and unsuccessful search lengths is presented. The experimental and analytical results demonstrate the reductions possible. This method does not restrict the hashing table configuration parameters and util ..."
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A novel extension to external double hashing providing significant reduction to both successful and unsuccessful search lengths is presented. The experimental and analytical results demonstrate the reductions possible. This method does not restrict the hashing table configuration parameters and utilizes very little additional storage space per bucket. The runtime performance for insertion is slightly greater than for ordinary external double hashing. 1 1.
Abstract How Caching Affects Hashing ∗
"... A number of recent papers have considered the influence of modern computer memory hierarchies on the performance of hashing algorithms [1, 2, 3]. Motivation for these papers is drawn from recent technology trends that have produced an everwidening gap between the speed of CPUs and the latency of dy ..."
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A number of recent papers have considered the influence of modern computer memory hierarchies on the performance of hashing algorithms [1, 2, 3]. Motivation for these papers is drawn from recent technology trends that have produced an everwidening gap between the speed of CPUs and the latency of dynamic random access memories. The result is an emerging computing folklore which contends that inferior hash functions, in terms of the number of collisions they produce, may in fact lead to superior performance because these collisions mainly occur in cache rather than main memory. This line of reasoning is the antithesis of that used to justify most of the improvements that have been proposed for open address hashing over the past forty years. Such improvements have generally sought to minimize collisions by spreading data elements more randomly through the hash table. Indeed the name “hashing � itself is meant to convey this notion [12]. However, the very act of spreading the data elements throughout the table negatively impacts their degree of spatial locality in computer memory, thereby increasing the likelihood of cache misses during long probe sequences. In this paper we study the performance tradeoffs that exist when implementing open address hash functions on contemporary computers. Experimental analyses are reported that make use of a variety of different hash functions, ranging from linear probing to highly “chaotic� forms of double hashing, using data sets that are justified through informationtheoretic analyses. Our results, contrary to those in a number of recently published papers, show that the savings gained by reducing collisions (and therefore probe sequence lengths) usually compensate for any increase in cache misses. That is, linear probing is usually no better than, and in some cases performs far worse than double hash functions that spread data more randomly through the table. to us. ∗ We wish to thank to Bernard Moret for suggesting this topic