  Hashing with linear probing dates back to the 1950s, and is among the most
studied algorithms. In recent years it has become one of the most important
hash table organizations since it uses the cache of modern computers very well.
Unfortunately, previous analysis rely either on complicated and space consuming
hash functions, or on the unrealistic assumption of free access to a truly
random hash function. Already Carter and Wegman, in their seminal paper on
universal hashing, raised the question of extending their analysis to linear
probing. However, we show in this paper that linear probing using a pairwise
independent family may have expected {\em logarithmic} cost per operation. On
the positive side, we show that 5-wise independence is enough to ensure
constant expected time per operation. This resolves the question of finding a
space and time efficient hash function that provably ensures good performance
for linear probing.
