Query Execution Two-pass Algorithms based on Hashing By Swathi Vegesna

At a glimpse Introduction Partitioning Relations by Hashing Algorithm for Duplicate Elimination Grouping and Aggregation Union, Intersection, and Difference Hash-Join Algorithm Sort based Vs Hash based Summary

Introduction Hashing is done if the data is too big to store in main memory buffers. Hash all the tuples of the argument(s) using an appropriate hash key. For all the common operations. there is a way to select the hash key so all the tuples that need to be considered together when we perform the operation have the same hash value. This reduces the size of the operand(s) by a factor equal to the number of buckets.

Partitioning Relations by Hashing Algorithm: initialize M-1 buckets using M-1 empty buffers; FOR each block b of relation R DO BEGIN read block b into the Mth buffer; FOR each tuple t in b DO BEGIN IF the buffer for bucket h(t) has no room for t THEN BEGIN copy the buffer t o disk; initialize a new empty block i n t h a t buffer; END; copy t to the buffer for bucket h(t); END ; FOR each bucket DO IF the buffer for t h is bucket is not empty THEN write the buffer to disk;

Duplicate Elimination For the operation δ(R) hash R to M-1 Buckets. (Note that two copies of the same tuple t will hash to the same bucket) Do duplicate elimination on each bucket Ri independently, using one-pass algorithm The result is the union of δ(Ri), where Ri is the portion of R that hashes to the ith bucket

Requirements Number of disk I/O's: 3*B(R) B(R) < M(M-1), only then the two-pass, hash-based algorithm will work In order for this to work, we need: hash function h evenly distributes the tuples among the buckets each bucket Ri fits in main memory (to allow the one-pass algorithm) i.e., B(R) ≤ M2

Grouping and Aggregation Hash all the tuples of relation R to M-1 buckets, using a hash function that depends only on the grouping attributes (Note: all tuples in the same group end up in the same bucket) Use the one-pass algorithm to process each bucket independently Uses 3*B(R) disk I/O's, requires B(R) ≤ M2

Union, Intersection, and Difference For binary operation we use the same has function to hash tuples of both arguments. R U S we hash both R and S to M-1 R S we hash both R and S to 2(M-1) R-S we hash both R and S to 2(M-1) Requires 3(B(R)+B(S)) disk I/O’s. Two pass hash based algorithm requires min(B(R)+B(S))≤ M2

Hash-Join Algorithm Use same hash function for both relations; hash function should depend only on the join attributes Hash R to M-1 buckets R1, R2, …, RM-1 Hash S to M-1 buckets S1, S2, …, SM-1 Do one-pass join of Ri and Si, for all i 3*(B(R) + B(S)) disk I/O's; min(B(R),B(S)) ≤ M2

Sort based Vs Hash based For binary operations, hash-based only limits size to min of arguments, not sum Sort-based can produce output in sorted order, which can be helpful Hash-based depends on buckets being of equal size Sort-based algorithms can experience reduced rotational latency or seek time

Summary Partitioning Relations by Hashing Algorithm for Duplicate Elimination Grouping and Aggregation Union, Intersection, and Difference Hash-Join Algorithm Sort based Vs Hash based

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