Figure 7 shows experimentally determined values for the average number of probes
during insertion for various schemes and load factors below 1/2. We disregard reads
and writes to locations known to be in cache, and the cost of rehashes. Measurements
were made in “equilibrium” after 105 insertions and deletions, using tables of size 215
and truly random hash function values. We believe that this curve is independent of the
table size (up to vanishing terms). The curve for LINEAR PROBING does not appear, as
the number of non-cached memory accesses depends on cache architecture (length of the
cache line), but it is typically very close to 1. The curve for CUCKOO HASHING seems to
be 2 + 1/(4 + 8α) ≈ 2 + 1/(4ε). This is in good correspondence with (3) of the analysis
in Section 2.3. It should be remarked that the highest possible load factor for TWO-WAY
CHAINING is O(1/ loglog n).