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 ever-widening 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 information-theoretic 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. ∗We wish to thank to Bernard Moret for suggesting this topic to us. Thus, for general-purpose use, a practitioner is well-advised to choose double hashing over linear probing. Explanations are provided as to why these results differ from those previ-