Presented By: Seungbeom Ma (ID 125)
Professor: Dr. T. Y. Lin
Computer Science Department
San Jose State University

 Previously , most of algorithms are required two passes.
 There is a case that we need more than two passes.
 Case : Data is too big to store in main memory.
 We have to hash or sort the relation with multipass algorithms.

 1. Multipass Sort-Based Algorithm
 2.
Multipass Hash-Based Algorithm

Multipass sort-based algorithm.
 M: Number of Memory Buffers
 R: Relation
 B(R) : Number of blocks for holding relation.
 BASIS:
 1. If R fits in M block (B (R) <= M).
 2. Reading R into main memory.
 3. Sorting R in the main memory with any sorting algorithm.
 4. Write the sorted relation to disk.

Multipass sort-based algorithm.
 INDUCTION: (B(R)> M)
 1. If R does not fit into main memory then partitioning the blocks hold R into M groups, which call R
1
, R
2
, …, R
M
 2.Recursively sorting R i from i =1 to M
 3.Once sorting is done, the algorithm merges the M sorted sublists.

Performance: Multipass Sort-Based Algorithms
1) Each pass of a sorting algorithm:
1.Reading data from the disk.
2. Sorting data with any sorting algorithms
3. Writing data back to the disk.
2-1) (k)-pass sorting algorithm needs
2k B(R) disk I/O’s
2-2)To calculate (Multipass)-pass sorting algorithm needs
= > A+ B
A: 2(K-1 ) (B(R) + B(S) ) [ disk I/O operation to sort the sublists]
B: B(R) + B(S)[ disk I/O operation to read the sorted the sublists in the final pass]
Total: (2k-1)(B(R)+B(S)) disk I/O’s

Multipass Hash-Based Algorithms
 1. Hashing the relations into M-1 buckets, where M is number of memory buffers.
 2. Unary case:
 It applies the operation to each bucket individually.
 1.Duplicate elimination (
δ
) and grouping (
γ
).
 1) Grouping: Min, Max, Count , Sum , AVG , which can group the data in the table
 2) Duplicate elimination: Distinct
Basis:
If the relation fits in M memory block,
-> Reading relation into memory and perform the operations.
 3. Binary case: It applies the operation to each corresponding pair of buckets.
 Query operations: union, intersection, difference , and join
 If either relations fits in M-1 memory blocks,
 -> Reading that relation into main memory M-1 blocks
 -> Reading next relation to 1 block at a time into the M th block
 Then performing the operations.

INDUCTION
 If Unary and Binary relation does not fit into the main memory buffers.
1.
Hashing each relation into M-1 buckets.
2.
Recursively performing the operation on each bucket or corresponding pair of buffers.
3.
Accumulating the output from each buckets or pair.

Hash-Based Algorithms : Unary Operatiors

Perfermance: Hash-Based Algorithms
 R: Realtion.
 Operations are like δ and γ
 M: Buffers
 U(M, k): Number of blocks in largest relation with k-pass hashing algorithm.

Performance: Induction
Induction:
1. Assuming that the first step divides relation R into M-1 equal buckets.
2. The buckets for the next pass must be small enough to handle in k-1 passes
3.Since R is divided into M-1 buckets , we need to have (M-1)u(M, k-1).

Sort-Based VS Hash-Based
1. Sort-based can produce output in sorted order. It might be helpful to reduce rotational latency or seek time
2. Hash-based depends on buckets being of equal size. For binary operations, hash-based only limits size of smaller relation. Therefore, hash-based can be faster than sort-based for small size of relation.

THANKS