design of hashing algorithms
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Figure 1. Time expense of random lookups on the ALPHA. The X-axis is the logarithm of
table space in bytes. The Y-axis is the average time in nanoseconds to perform a lookup.
1-byte integer
2-byte integer
4-byte integer
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
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Figure 2. Time expense of insertions on the ALPHA. The X-axis is the load factor.
The Y-axis is the average time in nanoseconds to insert a key. Insertions start with
an empty table and end at the load factor on the X-axis. The table has 4M key slots.
chaining 2
double hashing
chaining 1
packed chaining
packed double hashing
liner probing
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Figure 3. Time expense of insertions on the ALPHA. The X-axis is the logarithm
of key set size. The Y-axis is the average time in nano-seconds to insert a key.
Insertions start with an empty table and end with a load factor of 0.2 for chaining
and double hashing and 0.5 for linear probing, packed chaining and packed double hasing.
chaining
double hashing
packed chaining
packed double hashing
linear probing
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Figure 4. Average number of probes and jumps per insertion using closed
hashing. The X-axis is the load factor. The table has 4M key slots.
packed double hashing (probe)
linear probing (probe)
double hashing (probe and jump)
linear probing (jump)
packed double hashing (jump)
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0
0.5
1.0
1.5
2.0
2.5
Figure 5. Average number of probes and jumps per insertion using
chaining. The X-axis is the load factor. The table has 4M key slots.
packed chaining (probe)
chaining (probe and jump)
packed chaining (jump)
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.5
1.0
1.5
2.0
2.5
Figure 6. Average number of cache misses per insertion.
The X-axis is the load factor. The table has 4M key slots.
double hashing
linear probing
packed double hashing
chaining
packed chaining