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Like the merge join algorithm, the hash join algorithm can be used to implement natural joins and equi-joins In the hash join algorithm, a hash function h is used to partition tuples of both relations The basic idea is to partition the tuples of each of the relations into sets that have the same hash value on the join attributes We assume that h is a hash function mapping JoinAttrs values to {0, 1, , nh }, where JoinAttrs denotes the common attributes of r and s used in the natural join Hr0 , Hr1 , , Hrnh denote partitions of r tuples, each initially empty Each tuple tr r is put in partition Hri , where i = h(tr [JoinAttrs]) Hs0 , Hs1 , , Hsnh denote partitions of s tuples, each initially empty Each tuple ts s is put in partition Hsi , where i = h(ts [JoinAttrs]) The hash function h should have the goodness properties of randomness and uniformity that we discussed in 12 Figure 138 depicts the partitioning of the relations The idea behind the hash join algorithm is this: Suppose that an r tuple and an s tuple satisfy the join condition; then, they will have the same value for the join attributes If that value is hashed to some value i, the r tuple has to be in Hri and the s tuple in Hsi Therefore, r tuples in Hri need only to be compared with s tuples in Hsi ; they do not need to be compared with s tuples in any other partition For example, if d is a tuple in depositor, c a tuple in customer, and h a hash function on the customer-name attributes of the tuples, then d and c must be tested only if
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0 1 2 3 s 4 partitions of s
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Hash partitioning of relations
h(c) = h(d) If h(c) = h(d), then c and d must have different values for customer-name However, if h(c) = h(d), we must test c and d to see whether the values in their join attributes are the same, since it is possible that c and d have different customer-names that have the same hash value Figure 139 shows the details of the hash join algorithm to compute the natural join of relations r and s As in the merge join algorithm, tr 1 ts denotes the concatenation of the attributes of tuples tr and ts , followed by projecting out repeated attributes After the partitioning of the relations, the rest of the hash join code performs a separate indexed nested-loop join on each of the partition pairs i, for i = 0, , nh To do so, it rst builds a hash index on each Hsi , and then probes (that is, looks up Hsi ) with tuples from Hri The relation s is the build input, and r is the probe input The hash index on Hsi is built in memory, so there is no need to access the disk to retrieve the tuples The hash function used to build this hash index is different from the hash function h used earlier, but is still applied to only the join attributes In the course of the indexed nested-loop join, the system uses this hash index to retrieve records that will match records in the probe input The build and probe phases require only a single pass through both the build and probe inputs It is straightforward to extend the hash join algorithm to compute general equi-joins The value nh must be chosen to be large enough such that, for each i, the tuples in the partition Hsi of the build relation, along with the hash index on the partition, will t in memory It is not necessary for the partitions of the probe relation to t in memory Clearly, it is best to use the smaller input relation as the build relation If the size of the build relation is bs blocks, then, for each of the nh partitions to be of size less than or equal to M , nh must be at least bs /M More precisely stated, we have
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