Dr. Marina Gavrilova CPSC 335 Computer Science University of Calgary Canada

Outline Perfect Hashing Cichelli’s Algorithm

Perfect Hashing A perfect hashing function maps a key into a unique address. If the range of potential addresses is the same as the number of keys, the function is a minimal (in space) perfect hashing function. What makes perfect hashing distinctive is that it is a process for mapping a key space to a unique address in a smaller address space, that is hash (key) unique address Not only does a perfect hashing function improve retrieval performance, but a minimal perfect hashing function would provide 100 percent storage utilization.

Perfect Hashing Process of creating a perfect hash function A general form of a perfect hashing function is: p.hash (key) =(h0(key) + g[h1(key)] + g[h2(key)] mod N

Cichelli’s Algorithm In Cichelli’s algorithm, the component functions are: h0 = length (key) h1 = first_character (key) h2 = last_character (key) and g = T (x) where T is the table of values associated with individual characters x which may apply in a key. The time consuming part of Cichelli’s algorithm is determining T.

Cichelli’s Algorithm Table 1: Values associated with the characters of the Pascal reserved words When we apply the Cichelli’s perfect hashing function to the keyword begin using table 1, we can get – The keyword begin would be stored in location 33. Since the hash values run from 2 through 37 for this set of data, the hash function is a minimal perfect hashing function.

Cichelli’s Algorithm Cichelli’s algorithm for determining a perfect hash function

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