Linear probing — where it appears
Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.
The probe formula nobody checks
The expected number of probes to insert into a hash table under linear probing is ½(1 + 1/(1−α)²). It is quoted constantly, it is correct, and applied to a table of 256 slots at 95% load it overstates the measured cost by nearly half — because it is an asymptotic result and a real table is not asymptotic.
The probe nobody waits for
Robin Hood hashing makes an inserting key steal a slot from a key that has probed less far. The mean number of probes afterwards is 4.817, and before it was 4.817 — identical, and it cannot be otherwise, because the total displacement is fixed by the hash. What changes is the worst case, from 114 slots from home to 19, and a table reported by its average lookup cost shows no difference at all.
Two probes are two misses
Cuckoo hashing's lookup reads at most two slots, and at a load of 0.45 it reads 1.27 on average where linear probing reads 1.39. Replayed through a cache, it misses 1.18 times a lookup where linear probing misses 0.98. The table that wins the count the analysis uses loses the count the machine charges, because two slots in unrelated places are two cache lines, and a run of adjacent slots is usually one.
The bucket that fits a line
Make each of a cuckoo table's two candidates a bucket of eight slots laid out on one cache line, and no lookup ever touches more than two lines, the table builds past a load of 0.95, and at that load it misses 1.21 times a lookup where linear probing misses 1.79. The prediction that it would lose to linear probing at low loads was wrong — it misses less at every load measured, 0.94 against 0.96 at 0.3 — because a key it holds almost never lives in its second bucket. The guarantee belongs to the alignment, not the bucket; eight slots on lines of four put a lookup on four lines.
Named alongside it
The objects these essays reach for when they reach for this one.
Hash tableLoad factorCacheChained hashingCuckoo hashingLocalityMemory layoutMiss rateWorst case guaranteeAccess patternClosed formDisplacement