1. Additional notes on Hashing And notes on HW4

2. Selected Answers to the Last Assignment The records will hash to the following buckets: K h(K) (bucket number) 2369 1 3760 0 4692 4 4871 7 5659 3 1821 5 1074 2 7115 3 1620 4 2428 4 overflow 3943 7 4750 6 6975 7 overflow 4981 5 9208 0 Two records out of 15 are in overflow, which will require an additional block access. The other records require only one block access. Hence, the average time to retrieve a random record is: (1 * (13/15)) + (2 * (2/15)) = 0.867 + 0.266 = 1.133 block accesses

3. Now if you were asked to do this with extendible hashing record1 2369 1 00001 record2 3760 16 10000 record3 4692 20 10100 record4 4871 7 00111 record5 5659 27 11011 record6 1821 29 11101 record7 1074 18 10010 record8 7115 11 01011 record9 1620 20 10100 record10 2428 28 11100 record11 3943 7 00111 record12 4750 14 01110 record13 6975 31 11111 record14 4981 21 10101 record15 9208 24 11000

4. Lets go through the first few steps K mod 2 (2369 and 4871) in bucket 1, (3760 and 4692) in bucket 0. Now the next record is going to cause a split to K mod 4 – The key in extendible hashing is only the bucket that overflow needs to be split – for the other buckets you just use pointer de-referencing – record 5659 – will leave bucket 0 unchanged but the pointer derferences will need to be fixed – Hash element 00 will both point to bucket 0 – Hash element 11 will point to the bucket containing records 4871 and 5659 (both ending in 11) and Hash element 01 will point to record containing 2369. – Then 1821 will get added to the bucket containing 2369. – Now adding 1074 – the hash entry 10 will point to the new block containing this element – Now adding record 8 (01011) will cause a split and we will need to go to K Mod 8. – And so on.

5. Now if you were to do extendible hashing by remapping (linear hash) This one simply remaps all the data from scratch while using the next hash function K mod 2, K mod 4, K mod 8 The tradeoff is access cost is fixed constant – no dereferencing – The disadvantage is remapping frequently.