Chapter 12 Indexing and Hashing Cnt Basic Concepts Ordered Indices B Tree Index Files B Tree Index Files Static Hashing Dynamic Hashing Comparison of Ordered Indexing and Hashing Index Definition in SQL Multiple Key Access Database Management Systems 3ed R Ramakrishnan and J Gehrke 1 Dynamic Hashing Good for database that grows and shrinks in size Allows the hash function to be modified dynamically Extendable hashing one form of dynamic hashing Hash function generates values over a large range typically b bit integers with b 32 At any time use only a prefix of the hash function to index into a table of bucket addresses Let the length of the prefix be i bits 0 i 32 Bucket address table size 2i Initially i 0 Value of i grows and shrinks as the size of the database grows and shrinks Multiple entries in the bucket address table may point to a bucket Thus actual number of buckets is 2i The number of buckets also changes dynamically due to coalescing and splitting of buckets Database Management Systems 3ed R Ramakrishnan and J Gehrke 2 General Extendable Hash Structure In this structure i2 i3 i whereas i1 i 1 see next slide for details Database Management Systems 3ed R Ramakrishnan and J Gehrke 3 Use of Extendable Hash Structure Example Initial Hash structure bucket size 2 Database Management Systems 3ed R Ramakrishnan and J Gehrke 4 Example Cont Hash structure after insertion of one Brighton and two Downtown records Brighton Downtown 0010 1010 Database Management Systems 3ed R Ramakrishnan and J Gehrke 5 Example Cont Hash structure after insertion of Mianus record Brighton Downtown Mianus 0010 1010 1100 Database Management Systems 3ed R Ramakrishnan and J Gehrke 6 Example Cont Brighton Downtown Mianus Perryridge 0010 1010 1100 1111 Hash structure after insertion of three Perryridge records Database Management Systems 3ed R Ramakrishnan and J Gehrke 7 Example Cont Brighton Downtown Mianus Perryridge 0010 1010 1100 Redwood 0011 1111 Round 1101 Hash structure after insertion of Redwood and Round Hill records Database Management Systems 3ed R Ramakrishnan and J Gehrke 8 Use of Extendable Hash Structure Each bucket j stores a value ij all the entries that point to the same bucket have the same values on the first ij bits To locate the bucket containing search key Kj 1 Compute h Kj X 2 Use the first i high order bits of X as a displacement into bucket address table and follow the pointer to appropriate bucket To insert a record with search key value Kj follow same procedure as look up and locate the bucket say j If there is room in the bucket j insert record in the bucket Else the bucket must be split and insertion re attempted next slide Overflow buckets used instead in some cases as the case for Perryridge in previous example Database Management Systems 3ed R Ramakrishnan and J Gehrke 9 Updates in Extendable Hash Structure To split a bucket j when inserting record with search key value Kj If i ij more than one pointer to bucket j allocate a new bucket z and set ij and iz to the old ij 1 make the second half of the bucket address table entries pointing to j to point to z remove and reinsert each record in bucket j recompute new bucket for Kj and insert record in the bucket further splitting is required if the bucket is still full If i ij only one pointer to bucket j increment i and double the size of the bucket address table replace each entry in the table by two entries that point to the same bucket recompute new bucket address table entry for Kj Now i ij so use the first case above Database Management Systems 3ed R Ramakrishnan and J Gehrke 10 Updates in Extendable Hash Structure Cont When inserting a value if the bucket is full after several splits that is i reaches some limit b create an overflow bucket instead of splitting bucket entry table further To delete a key value locate it in its bucket and remove it The bucket itself can be removed if it becomes empty with appropriate updates to the bucket address table Coalescing of buckets can be done can coalesce only with a buddy bucket having same value of ij and same ij 1 prefix if it is present Decreasing bucket address table size is also possible Note decreasing bucket address table size is an expensive operation and should be done only if number of buckets becomes much smaller than the size of the table Database Management Systems 3ed R Ramakrishnan and J Gehrke 11 Extendable Hashing vs Other Schemes Benefits of extendable hashing Hash performance does not degrade with growth of file Minimal space overhead Disadvantages of extendable hashing Extra level of indirection to find desired record Bucket address table may itself become very big larger than memory Need a tree structure to locate desired record in the structure Changing size of bucket address table is an expensive operation Linear hashing is an alternative mechanism which avoids these disadvantages at the possible cost of more bucket overflows Database Management Systems 3ed R Ramakrishnan and J Gehrke 12 Comparison of Ordered Indexing and Hashing Cost of periodic re organization Relative frequency of insertions and deletions Is it desirable to optimize average access time at the expense of worst case access time Expected type of queries Hashing is generally better at retrieving records having a specified value of the key If range queries are common ordered indices are to be preferred Database Management Systems 3ed R Ramakrishnan and J Gehrke 13 Index Definition in SQL Create an index create index index name on relation name attribute list E g create index b index on branch branch name Use create unique index to indirectly specify and enforce the condition that the search key is a candidate key To drop an index drop index index name Database Management Systems 3ed R Ramakrishnan and J Gehrke 14 Multiple Key Access Use multiple indices for certain types of queries Example select account number from account where branch name Perryridge and balance 1000 Possible strategies for processing query using indices on single attributes 1 Use index on branch name to find accounts with branch name of Perryridge test balance 1000 2 Use index on balance to find accounts with balances of 1000 test branch name Perryridge 3 Use branch name index to find pointers to all records pertaining to the Perryridge branch Similarly use index on balance Take intersection of both sets of pointers obtained Database Management Systems 3ed R Ramakrishnan and J Gehrke 15 Indices on Multiple Attributes