1. HASHING PROJECT 1

2. SEARCHING DATA STRUCTURES Consider a set of data with N data items stored in some data structure We must be able to insert, delete & search for items What are possible ways to do this? What is the complexity of each structure & method ? 2

3. DATA STRUCTURES Unsorted Array Sorted Array Linked List Binary Search Tree Heap What are advantages & disadvantages of each? Time complexities of each? What about memory requirements? 3

4. SOFTWARE DEVELOPMENT Ask THESE questions – always! What if a data structure already exists & you MUST use it? Must be able to use most efficiently. 4

5. HASHING Technique for data storage & retrieval having constant time Do you believe it??? Perfect Hashing fits this definition, but not hashing in general 5

6. HASHING A storage & retrieval technique in which a data item (key) is converted to the address in which it will be stored. The same conversion is used to retrieve the data. Example – MSU M-number – 8 digits – index into an array Phone numbers? Problem? 6

7. HASH FUNCTION Mathematical operation which converts a search key into a hash table address Modulo functions is OFTEN used as part of the hash function Examples: M-number ~ Table size 7

8. COLLISION A collision occurs when 2 different search keys hash to the same table address. Collision Resolution Policy (CRP) – strategy for selecting an alternate location for the hashed item that cannot be placed in the computed table address CRP – affects the complexity of the hashing process Examples 8

9. OPEN ADDRESSING - CRP Select an alternate location in the table Linear Probing – beginning at original hash location, sequentially search the table for available location. {+1} Incremental probing - use a value other than 1 Double Hashing – use a second function to determine the probe increment {+f(n)} 9

10. OTHER CRP Bucket Hashing – Each hash address is actually a set of table locations Chaining – a linked list at each hash address contains all keys that hash there Table format for each? 10

11. TABLE SIZE?? How big should a hash table be? How full should the table get? Implications of table size? 11

12. MEASURING HASH PERFORMANCE Hash Function Complexity? Probes: number of hash table locations “probed” (checked) before finding an empty location (CRP) Consider AVERAGE for a large data set Table size: want smallest that provides few probes 12

13. OUR SEMESTER PROJECT – HASHING Analysis Empirical Studies Table Sized CRP’s Functions 13