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Semester 2/Database Systems/Week 10/Week 10 Database Systems.md

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+# Query Optimisation Revision
+
+1. Obtaining the desired information from a database system in a predictable and reliable fashion is Query Processing. Getting these results back in a timely manner deals with the technique of Query Optimization.
+2. r(rID, rName, rDescription), 5000 tuples.
+   tuple header(24b)
+   rID(6b)
+   rName(10b)
+   rDescription(100b)
+   Disc Block(1024b)
+   Disc Block Header(24b)
+   Block Space 1000b
+	1. (24+6+10+100)=140b
+	   We can fit 7 tuples in 1 block.
+	   5000/7 = 715 blocks required.
+	2. (24+6+10) = 40b
+	   25 tuples per block
+	   5000/25 = 200 blocks required.
+	3. Since the projection uses significantly less blocks, we access the disc less in queries compared to using every attribute. 715/200 = 3.6x less disc block accesses.
+3. Write relational algebra expressions for the following SQL query.
+   SELECT lecturers.name, students.name, courses.name
+   FROM lecturers, students, assessors, courses
+   WHERE lecturers.lid=assessors.lid
+   AND students.sid=assessors.sid
+   AND students.cid=courses.cid
+   AND courses.cid=“CS”;
+		π lecturers.name, students.name, courses.name (
+		    σ courses.cid = "CS" (
+		        lecturers ⨝ (
+		            assessors ⨝ (
+		                students ⨝ courses))))
+		Or,
+		π lecturers.name, students.name, courses.name
+			(σ lecturers.lid=assessors.lid
+				(σ students.sid=accessors.sid
+					(σ courses.cid=students.did
+						(σ courses.cid='CS'(courses\*students)
+					)\* assessors
+				)\* lecturers
+			)
+	1. Draw query tree
+	   
+4. List heuristics that optimisers apply to reduce cost of optimisation.
+	- Begin with initial query tree for SQL
+	- Move SELECT operations down the tree
+	- Apply more restrictive SELECT operations first ( eg. equalities before range queries )
+	- Replace Cartesian products followed by selection with theta joins ( eg. *sigma(f) ( RxS )* -> *R theta(f) S* )
+	- Move PROJECT operations down the query tree ( add project operations as inputs to theta joins ).
+5. Draw a near optimal query tree for the following:
+   SELECT hotels.name 
+   FROM hotels, ratings 
+   WHERE hotels.rid=ratings.rid 
+   AND hotels.hid=10 
+   AND ratings.rating>7;
+   1. Write relational algebra expressions for this tree
+
+
+# Precedence Graphs Revision
+
+1. State True / False
+	1. A transaction in which all steps must be completed successfully or none of them will be completed is called a durable transaction.
+	   False, this is the definition of an atomic transaction
+	2. Two-phased locking can be used to ensure that transactions are serializable
+	   True
+	3. Although two transactions may be correct in themselves, interleaving of operations may produce an incorrect result.
+	   True
+	4. Transactions should be written to the log before they are applied to the database itself.
+	   True
+2. Consider the following precedence graph for a non-serial schedule consisting of four transactions. Is the corresponding schedule conflict serializable? Justify your answer. If it is conflict-serializable give a corresponding serial schedule.
+   ![](Pasted%20image%2020240319160609.png)
+   The following is serialisable, since there are no cycles in the precedence graph. T1, T2, T3, T4.
+   3. For each of the schedules shown in Table 36.1, draw a precedence graph, determine whether it is conflict serializable and justify your answer.
+    ![](Pasted%20image%2020240319161202.png)
+    ![](Pasted%20image%2020240319162824.png)
+    Not serialisable, directed cycle in graph.
+    ![](Pasted%20image%2020240319163053.png)
+    Not serialisable, directed cycle in graph
+