Hash join
The hash join is an example of a join algorithm and is used in the implementation of a relational database management system. All variants of hash join algorithms involve building hash tables from the tuples of one or both of the joined relations, and subsequently probing those tables so that only tuples with the same hash code need to be compared for equality in equijoins. Hash joins are typically more efficient than nested loops joins, except when the probe side of the join is very small. They require an equijoin predicate (a predicate comparing records from one table  with those from the other table using a conjunction of equality operators '=' on one or more columns). Classic hash join. The classic hash join algorithm for an inner join of two relations proceeds as follows: The first phase is usually called the "build" phase, while the second is called the "probe" phase. Similarly, the join relation on which the hash table is built is called the "build" input, whereas the other input is called the "probe" input. This algorithm is simple, but it requires that the smaller join relation fits into memory, which is sometimes not the case. A  simple approach to handling this situation proceeds as follows: This is essentially the same as the block nested loop join algorithm. This algorithm scans formula_4 eventually more times than necessary. Grace hash join. A better approach is known as the "grace hash join", after the GRACE database machine for which it was first implemented. This algorithm avoids rescanning the entire formula_4 relation by first partitioning both formula_2 and formula_4 via a hash function, and writing these partitions out to disk. The algorithm then loads pairs of partitions into memory, builds a hash table for the smaller partitioned relation, and probes  the other relation for matches with the current hash table. Because the partitions were formed by hashing on the join key, it must be the case that any join output tuples must belong to the same partition. It is possible that one or more of the partitions still does not fit into the available memory, in which case the algorithm is recursively applied: an additional orthogonal hash function is chosen to hash the large partition into sub-partitions, which are then processed as before. Since this is expensive, the algorithm tries to reduce the chance that it will occur by  forming the smallest partitions possible during the initial partitioning phase. Hybrid hash join. The hybrid hash join algorithm is a refinement of the grace hash join which takes advantage of more available memory. During the partitioning phase, the hybrid hash join uses the available memory for two purposes: Because partition 0 is never written to or read from disk, the hybrid hash join typically performs fewer I/O operations than the grace hash join. Note that this algorithm is memory-sensitive, because there are two competing demands for memory (the hash table for partition 0, and the output buffers for  the remaining partitions). Choosing too large a hash table might cause the algorithm to recurse because one of the non-zero partitions is too large to fit into memory. Hash anti-join. Hash joins can also be evaluated for an anti-join predicate (a predicate selecting values from one table when no related values are found in the other). Depending on the sizes of the tables, different algorithms can be applied: Hash left anti-join. This is more efficient when the NOT IN table is smaller than the FROM table Hash right anti-join. This is more efficient when the  NOT IN table is larger than the FROM table Hash semi-join. Hash semi-join is used to return the records found in the other table. Unlike plain join, it returns each matching record from the leading table only once, not regarding how many matches are there in the IN table. As with the anti-join, semi-join can also be left and right: Hash left semi-join. The records are returned right after they produced a hit. The actual records from the hash table are ignored. This is more efficient when the IN table is smaller than the FROM  table Hash right semi-join. With this algorithm, each record from the hash table (that is, FROM table) can only be returned once, since it is removed after being returned. This is more efficient when the IN table is larger than the FROM table