Question 1 (a) 10 marks

Transcription

1 Question 1 (a) Consider the tree in the next slide. Find any/ all violations of a B+tree structure. Identify each bad node and give a brief explanation of each error. Assume the order of the tree is 4 (n=4; 4 keys, 5 pointers.) 10 marks

2 The B+tree... not half-full duplicate key swapped positions not less than root not less than parent

3 Question 1 (b) Consider a relation R(A, B) stored using a partitioned hash organization. The hash table contains 1024 blocks (buckets), and the tuples (records) are stored in these blocks. To store tuple (a, b), we apply hash function h 1 for a, obtaining X bits. Then, we apply hash function h 2 on b, obtaining 10-X bits. The bits are concatenated, obtaining a 10 bit hash value that identifies the block where (a, b) is placed. Suppose that 20% of the queries on R are of the form Q 1 : select * from R where A = a, and 80% of the queries are of the form Q 2 : select * from R where B = b where a and b are constants. How many blocks are accessed by Q 1 queries? How many by Q 2 queries? (Your answer should be a function of X.) (5 marks) Write an expression that gives the expected number of blocks that must be accessed (on average). (5 marks) What X value minimizes the expected number of I/Os? (Hint: Recall that the derivative (with respect to x) of 2 ax+b is a*2 ax+b *ln2.) (5 marks)

4 Answer to Q. 1 (b) Q1 queries touch as many blocks as there are bits dedicated in the hash function for Q2 2 (10-X) The remaining bits, are used for Q2 2 X On average, 20% of the queries for will touch Q1 blocks and 80% will touch Q2 blocks 0.2*2 (10-X) +0.8*2 X. Find the value of X that minimizes the average either by trial (X=1, 2, 3...) or by taking the derivative D and solving D=0 for X in both cases, X = 4

5 Question 2 Relational schema: emp(eid, did, salary, hobby) dept(did, dname, floor, phone) finance(did, budget, sales, expenses)

6 No indexes; nlj is the only available algorithm A good plan in relational algebra (2 marks) Possible query select D.dname, F.budget from Emp E, Dept D, Finance F where E.did = D.did and D.did = F.did and π dname, budget D.floor = 1 and E.sal >= and D.did = F.did E.hobby = 'yodelling' E.did = D.did σfloor = 1 σ sal>=59000 and π did, budget hobby= yodelling π sal, did, hobby E π did, dname, floor D F

7 Possible query How many plans in total? What is their shape? (2 marks) 12 plans in total; basically, all permutations of E, D and F (3! = 6) each permutation can be mapped to a left-deep or right-deep plan select D.dname, F.budget from Emp E, Dept D, Finance F where E.did = D.did and D.did = F.did and D.floor = 1 and E.sal >= and E.hobby = 'yodelling'

8 Available indexes Assume the following indexes can be built: Emp.did, Emp.sal, Dept.floor, Dept.did, Finance. did (all are integer fields) Which should be clustered and why? (2 marks) All key indexes should be clustered -- this is the natural clustering of the relations and there are no duplicates; whether Emp.did is clustered is an even bet, but it is a foreign key

9 Access path selection Assuming the clustered methods are the cheapest, what would the access path selection step of a System-R style optimiser be? (2 marks) Very simple: just enumerate all access methods per relation and propagate the clustered ones from the previous question How would the previous decision change if an order by Dept.floor clause is added? (2 marks) Dept.floor is now an interesting order, so the index on it is propagated as well

10 Statistics What are the cardinality estimates for the base relations after applying local predicates? (2 marks) s.f. of (E.sal > 59000) = ( )/( ) = 0.02 s.f. of (D.floor = 1) = 1/2 = 0.5 s.f. of (E.hobby = yodelling ) = 1/200 = Estimated card. for E = 0.02 * * 50,000 = 5 Estimated card. for D = 0.5 * 500 = 250 F remains unchanged (no local predicates) select D.dname, F.budget from Emp E, Dept D, Finance F where E.did = D.did and D.did = F.did and D.floor = 1 and E.sal >= and E.hobby = 'yodelling' The statistics of the system indicate that employee salaries range from 10,000 to 60,000, employees enjoy 200 different hobbies, and the company owns two floors in the building. There are a total of 50,000 employees and 500 departments

11 What is possibly the best plan? (E D) F; this minimises the cardinality of intermediate results and chooses the smaller relation as the outer one (card. of E = 5, card. of D = 250, card. of F = 5000) select D.dname, F.budget from Emp E, Dept D, Finance F where E.did = D.did and D.did = F.did and D.floor = 1 and E.sal >= and E.hobby = 'yodelling' Given the statistical estimates, and assuming only a index-nested-loops join available, what is most likely the best join order chosen by the optimiser? (4 marks)

12 Plan enumeration Emp.did nlj Dept.did (did order) Emp.did nlj Dept.floor (did order) Emp.did smj Dept.did (did.order) Emp.did smj sort Dept.did (Dept.floor) (did.order) Dept.did nlj Emp.did (did order) Dept.floor nlj Emp.did (floor order) Dept.did smj Emp.did (did order) sort Dept.did (Dept.floor) smj Emp.did (did order) Assuming sort-merge is also available and given the answer to the question after the order by clause is added, show the steps involved in the system's optimiser exploring the search space of Emp Dept and Dept Emp (8 marks)

13 Question 3 (a) Joe Student has come up with a new simplified concurrency control scheme. Instead of having IX and IS locks, he proposes only one intention lock, I. He also proposes an SIL lock (gives you shared access at the level it is granted, and permission to ask for another lock, shared or exclusive, at the lower levels.)

14 Question 3 (a) (i) NL S X IL SIL NL Y Y Y Y Y S Y Y N N N X Y N N N N What is the compatibility matrix? (5 marks) IL Y N N N N SIL Y N N N N

15 Question 3 (a) (ii) Joe's plan would definitely have lower concurrency, since it disallows locking combinations that would work with the scheme that distinguishes between IS and IX locks. Overhead is harder to answer; Most well-reasoned answers were accepted. The best answer is that the overhead is lower because most of the time transactions are waiting on lock conflicts, so they do not do as much setting and releasing of locks. Any answer making this observation should earn all five marks. How would you expect Joe's plan to perform with respect to concurrency and overhead when compared to the scheme discussed in class? (5 marks)

16 Question 3 (b) Consider the three points in time in the log: (i) beginning of analysis phase, (ii) beginning of the REDO phase, (iii) earliest log record considered by the UNDO phase. Is it possible that they could occur, from first to last, in the order (i), (ii), (iii)? Explain your answer. (5 marks)

17 Answer to Q. 3 (b) Yes, they could happen in that order. Suppose we have a completely quiet system, with no active transactions or dirty pages. Suppose at time t1, the system takes a checkpoint. At time t2 (t2 > t1), a transaction starts up, dirties a page, and commits. At time t3 (t3 > t2), another transaction starts up, and dirties a page, which is then flushed to disk. Then the system crashes. Then (a) is at t1, (b) is at t2, (c) is at t3