1CSE 326: Data StructuresTopic #10: Hashing (3)Ashish Sabharwal Autumn - PDF document

1CSE 326: Data StructuresTopic #10: Hashing (3)Ashish Sabharwal Autumn, 20032Today’s Outline•Admin:–Hardcopyturninfor Project 2 –now!–Homework 2due Friday–Start looking for a partnerfor Project 3(must be someone different from your Project 2 partner)•Finish Hashing–Double hashing, rehashing–Extendible hashing•Group Quiz #43When to Rehash?Many alternatives:•Rehash when table is half full•Rehash when insertion fails in open addressing•Rehash when insertion becomes very slowin separate chaining•Rehash when lcrosses a certain threshold4Something We Again Forgot:Disk Acesses5We Want To Minimize Disk Accesses!1024 bytes•Entire blocks transferred into memory at a time•Transfer time much lessthan seek time•Therefore we need to minimize disk accesses!Disk access time =Seek time+Transfer time6Solution: Extendible HashingHashing technique for huge data sets–Optimizes to reduce disk accesses Hash “table” contains1.Directory2Dentries, Dbits per entry, pointers to leaf buckets2.Leaf BucketsKeys in leaf Lhave dL£Dbits in common with parent key,leaves store all dataProperties–Only 2 levels in the table –only 2 disk accesses for find!–Each leaf bucket fits on one disk block –caching–Better than B-Trees if order is not important –why? 27001010011110111101Extendible Hash TableDirectory entry : key prefix(first Dbits) and a pointer to the bucketwith all keys starting with that prefixBucket entry : keys matching on first dL£Dbits, plus the dataassociated with those keys000100(dL= 2)00001000110010000110(dL= 2)010010101101100(dL= 3)1000110011(dL= 3)101011011010111(dL= 2)110011110011110Directory for D= 3insert(11010)?insert(11011)?+ data+ data+ data+ dataBucket size = 48001010011110111101Inserting Using Bucket-Split000100(dL= 2)00001000110010000110(dL= 2)010010101101100(dL= 3)1000110011(dL= 3)101011011010111(dL= 3)110011101011011Directory for D= 3+ data+ data+ data+ dataBucket size = 4(dL= 3)1110011110Split9Insertion Using Directory-Expansion1.insert(10010)But, no room to insert,only one parent,and no adoption!2.Solution: Expand directoryNow do a bucket-split01101100(2)01101(2)10000100011001110111(2)1100111110001010011110111101000100More expensive!How to ensure this is uncommon?D= 2D= 310What if Extendible HashingDoesn’t Cut It?Option 1: Store only pointers/references to the items: (key, value) pairs separately on diskOption 2: Improve hash function; Rehash11The One-Slide HashCollision resolution1.Separate Chaining–Expand beyond hashtablevia secondary Dictionaries–Allows l� 12.Open Addressing–Expand within hashtable–Secondary probing: {linear, quadratic, double hash}–l£1 (by definition!)–l£½ (by preference!)Choosing a Hash Function•Make sure table size is prime•Careful choice for strings•“Perfect hashing”–If keys known in advance, tune hash function for them!Rehashing•Tunes up hashtablewhen, e.g.,lcrosses a thresholdExtendible hashing•For disk-based dataHash function: maps keys to integers12Search ADT Implementations•Unsorted list(1)(n)(n)•Sorted list(n)(log n)?(n)•Trees(log n)(log n)(log n)•Hash Table(1)(1)(1)insertdeletefindIs there anything a hash table cannotdo efficiently?(average case)You’ll answer this in quiz #4!