Hashing gt1
- 1. HashingHashing Gaurav TrivediGaurav Trivedi EE 693EE 693 Algorithms and Data StructuresAlgorithms and Data Structures
- 2. ContentsContents Static HashingStatic Hashing • File OrganizationFile Organization • Properties of the Hash FunctionProperties of the Hash Function • Bucket OverflowBucket Overflow • IndicesIndices Dynamic HashingDynamic Hashing • Underlying Data StructureUnderlying Data Structure • Querying and UpdatingQuerying and Updating ComparisonsComparisons • Other types of hashingOther types of hashing • Ordered Indexing vs. HashingOrdered Indexing vs. Hashing
- 3. Static HashingStatic Hashing Hashing provides a means forHashing provides a means for accessing data without the use of anaccessing data without the use of an index structure.index structure. Data is addressed on disk byData is addressed on disk by computing a function on a searchcomputing a function on a search key instead.key instead.
- 4. OrganizationOrganization AA bucketbucket in a hash file is unit ofin a hash file is unit of storage (typically a disk block) thatstorage (typically a disk block) that can hold one or more records.can hold one or more records. TheThe hash functionhash function, h, is a function, h, is a function from the set of all search-keys, K, tofrom the set of all search-keys, K, to the set of all bucket addresses, B.the set of all bucket addresses, B. Insertion, deletion, and lookup areInsertion, deletion, and lookup are done in constant time.done in constant time.
- 5. Querying and UpdatesQuerying and Updates To insert a record into the structureTo insert a record into the structure compute the hash value h(Kcompute the hash value h(Kii), and), and place the record in the bucketplace the record in the bucket address returned.address returned. For lookup operations, compute theFor lookup operations, compute the hash value as above and search eachhash value as above and search each record in the bucket for the specificrecord in the bucket for the specific record.record. To delete simply lookup and remove.To delete simply lookup and remove.
- 6. Properties of the Hash FunctionProperties of the Hash Function The distribution should be uniform.The distribution should be uniform. • An ideal hash function should assign theAn ideal hash function should assign the same number of records in each bucket.same number of records in each bucket. The distribution should be random.The distribution should be random. • Regardless of the actual search-keys,Regardless of the actual search-keys, the each bucket has the same numberthe each bucket has the same number of records on averageof records on average • Hash values should not depend on anyHash values should not depend on any ordering or the search-keysordering or the search-keys
- 7. Bucket OverflowBucket Overflow How does bucket overflow occur?How does bucket overflow occur? • Not enough buckets to handle dataNot enough buckets to handle data • A few buckets have considerably moreA few buckets have considerably more records then others. This is referred torecords then others. This is referred to as skew.as skew. Multiple records have the same hash valueMultiple records have the same hash value Non-uniform hash function distribution.Non-uniform hash function distribution.
- 8. SolutionsSolutions Provide more buckets then areProvide more buckets then are needed.needed. Overflow chainingOverflow chaining • If a bucket is full, link another bucket toIf a bucket is full, link another bucket to it. Repeat as necessary.it. Repeat as necessary. • The system must then check overflowThe system must then check overflow buckets for querying and updates. Thisbuckets for querying and updates. This is known asis known as closed hashingclosed hashing..
- 9. AlternativesAlternatives Open hashingOpen hashing • The number of buckets is fixedThe number of buckets is fixed • Overflow is handled by using the nextOverflow is handled by using the next bucket in cyclic order that has space.bucket in cyclic order that has space. This is known asThis is known as linear probinglinear probing.. Compute more hash functions.Compute more hash functions. Note: Closed hashing is preferred inNote: Closed hashing is preferred in database systems.database systems.
- 10. IndicesIndices AA hash indexhash index organizes the searchorganizes the search keys, with their pointers, into a hashkeys, with their pointers, into a hash file.file. Hash indices never primary evenHash indices never primary even though they provide direct access.though they provide direct access.
- 11. Example of Hash IndexExample of Hash Index
- 12. Dynamic HashingDynamic Hashing More effective then static hashingMore effective then static hashing when the database grows or shrinkswhen the database grows or shrinks Extendable hashingExtendable hashing splits andsplits and coalesces buckets appropriately withcoalesces buckets appropriately with the database size.the database size. • i.e. buckets are added and deleted oni.e. buckets are added and deleted on demand.demand.
- 13. The Hash FunctionThe Hash Function Typically produces a large number ofTypically produces a large number of values, uniformly and randomly.values, uniformly and randomly. Only part of the value is usedOnly part of the value is used depending on the size of thedepending on the size of the database.database.
- 14. Data StructureData Structure Hash indices are typically a prefix ofHash indices are typically a prefix of the entire hash value.the entire hash value. More then one consecutive index canMore then one consecutive index can point to the same bucket.point to the same bucket. • The indices have the same hash prefixThe indices have the same hash prefix which can be shorter then the length ofwhich can be shorter then the length of the index.the index.
- 15. General Extendable HashGeneral Extendable Hash StructureStructure In this structure, i2 = i3 = i, whereas i1 = i – 1
- 16. Queries and UpdatesQueries and Updates LookupLookup • Take the first i bits of the hash value.Take the first i bits of the hash value. • Following the corresponding entry in theFollowing the corresponding entry in the bucket address table.bucket address table. • Look in the bucket.Look in the bucket.
- 17. Queries and Updates (Cont’d)Queries and Updates (Cont’d) InsertionInsertion • Follow lookup procedureFollow lookup procedure • If the bucket has space, add the record.If the bucket has space, add the record. • If not…If not…
- 18. Insertion (Cont’d)Insertion (Cont’d) Case 1: i = iCase 1: i = ijj • Use an additional bit in the hash valueUse an additional bit in the hash value This doubles the size of the bucket address table.This doubles the size of the bucket address table. Makes two entries in the table point to the fullMakes two entries in the table point to the full bucket.bucket. • Allocate a new bucket, z.Allocate a new bucket, z. Set iSet ijj and iand izz to ito i Point the second entry to the new bucketPoint the second entry to the new bucket Rehash the old bucketRehash the old bucket • Repeat insertion attemptRepeat insertion attempt
- 19. Insertion (Cont’d)Insertion (Cont’d) Case 2: i > iCase 2: i > ijj • Allocate a new bucket, zAllocate a new bucket, z • Add 1 to iAdd 1 to ijj, set, set iijj andand iizz to this new valueto this new value • Put half of the entries in the first bucketPut half of the entries in the first bucket and half in the otherand half in the other • Rehash records in bucket jRehash records in bucket j • Reattempt insertionReattempt insertion
- 20. Insertion (Finally)Insertion (Finally) If all the records in the bucket haveIf all the records in the bucket have the same search value, simply usethe same search value, simply use overflow buckets as seen in staticoverflow buckets as seen in static hashing.hashing.
- 21. Use of Extendable HashUse of Extendable Hash Structure: ExampleStructure: Example Initial Hash structure, bucket size = 2
- 22. Example (Cont.)Example (Cont.) Hash structure after insertion ofHash structure after insertion of one Brighton and two Downtownone Brighton and two Downtown recordsrecords
- 23. Example (Cont.)Example (Cont.) Hash structure after insertion of Mianus record
- 24. Example (Cont.)Example (Cont.) Hash structure after insertion of three Perryridge records
- 25. Example (Cont.)Example (Cont.) Hash structure after insertion ofHash structure after insertion of Redwood and Round Hill recordsRedwood and Round Hill records
- 26. Comparison to Other HashingComparison to Other Hashing MethodsMethods Advantage: performance does notAdvantage: performance does not decrease as the database sizedecrease as the database size increasesincreases • Space is conserved by adding andSpace is conserved by adding and removing as necessaryremoving as necessary Disadvantage: additional level ofDisadvantage: additional level of indirection for operationsindirection for operations • Complex implementationComplex implementation
- 27. Ordered Indexing vs. HashingOrdered Indexing vs. Hashing Hashing is less efficient if queries toHashing is less efficient if queries to the database include ranges asthe database include ranges as opposed to specific values.opposed to specific values. In cases where ranges are infrequentIn cases where ranges are infrequent hashing provides faster insertion,hashing provides faster insertion, deletion, and lookup then ordereddeletion, and lookup then ordered indexing.indexing.