5. Joins (between relations R and S, R = outer, S = inner) Cost
a. NLJ
i. Tuple-oriented NLJ
Cost = NPages(R) + NTuples(R) * NPages(S)
ii. Page-oriented NLJ
Cost = NPages(R) + NPages (R) * NPages(S)
iii. Block-oriented NJL (for block_size B)
Cost = NPages(R) + ceil(NPages (R)/(B-2)) * NPages(S)
b. Hash Join
Cost = 3*(NPages(R) + NPages(S))
c. Sort-Merge Join
CostSMJ = NPages(R) + NPages(S) + 
2* NPages(R)* num_passes(R) +
2* NPages(S)* num_passes(S).  Chatbot

Generalized Notes for Improvement
Understanding Multi-Pass Algorithms:
External Sorting: Accurately determine the number of passes based on buffer size and relation size. Recognize when more passes are required.
Hash Joins: Understand how buffer size impacts the number of hash partitions and whether a single-pass (in-memory) hash join is feasible.
Buffer Allocation and Its Impact:
Optimal Buffer Usage: Correctly allocate buffer pages between relations and output to minimize I/O costs.
Influence on Join Strategies: Recognize how available buffer space can transform the efficiency of join algorithms (e.g., enabling single-pass hash joins).
Accurate Cost Calculations:
Detailed Step-by-Step Analysis: Ensure each phase of the join algorithm is accounted for, including all read and write operations.
Scenario-Based Adjustments: Adapt cost calculations based on specific scenarios, such as large buffer sizes or the presence of indexes.
Algorithm Selection Based on Data and Resources:
Choosing the Most Efficient Algorithm: Identify the join strategy that offers the lowest cost based on the given data sizes and available buffer pages.
Flexibility in Approach: Be prepared to adjust the chosen algorithm parameters (like buffer allocation) to achieve optimal performance.
Verification Against Known Answers:
Cross-Checking Results: When discrepancies arise (as in this case), revisit the assumptions and calculations to identify and correct errors.
Understanding User Constraints: Pay close attention to specific constraints or hints provided to align the answer accordingly. Q1 Introduction (Total marks for Q1: 5 marks)
Consider two relations A and B. A has 80,000 tuples, and B has 100,000 tuples. Both relations store 100 tuples per page. Consider the following SQL statement:
SELECT *
FROM A INNER JOIN B

ON A.a = B.a;
We wish to evaluate an equijoin between A and B, with an equality condition A.a = B.a. There are 102 buffer pages available for this operation. Both relations are stored as (unsorted) heap files. Neither relation has any indexes built on it.
Consider the alternative join strategies described below and calculate the cost of each alternative. Evaluate the algorithms using the number of disk I/O's (i.e., pages) as the cost.
Page-oriented Nested Loops Join. Consider A as the outer relation. (1 mark)
Block-oriented Nested Loops Join. Consider A as the outer relation. (1 mark)
Sort-Merge Join. Assume that Sort-Merge Join can be done in 2 passes. (1 mark)
Hash Join (1 mark)
Assuming that no indexes are built on any of the two relations, and assuming that sufficient buffer space is available:
What would be the lowest possible cost to perform this query ? (0.5 mark)
What would be the minimum buffer size required to achieve this cost from 5A? (0.5 mark). YOU MUST USE THE ABOVE FORMULAS IN YOUR WORKING OUT