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The values are usually used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter-storage addressing. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval.
An important optimization, to reduce the effect of coalescing, is to restrict the address space of the hash function to only a subset of the table. For example, if the table has size M with buckets numbered from 0 to M − 1 , we can restrict the address space so that the hash function only assigns addresses to the first N locations in the table.
Generally, a new hash table with a size double that of the original hash table gets allocated privately and every item in the original hash table gets moved to the newly allocated one by computing the hash values of the items followed by the insertion operation. Rehashing is simple, but computationally expensive.
Pair-wise independence of the hash functions suffices. Like all other forms of open addressing, double hashing becomes linear as the hash table approaches maximum capacity. The usual heuristic is to limit the table loading to 75% of capacity. Eventually, rehashing to a larger size will be necessary, as with all other open addressing schemes.
In the simple case where the reduction function and the hash function have no collision, given a complete rainbow table (one that makes sure to find the corresponding password given any hash) the size of the password set |P|, the time T that had been needed to compute the table, the length of the table L and the average time t needed to find a ...
Setting this threshold close to zero and using a high growth rate for the table size leads to faster hash table operations but greater memory usage than threshold values close to one and low growth rates. A common choice would be to double the table size when the load factor would exceed 1/2, causing the load factor to stay between 1/4 and 1/2. [5]
Let p be the number of bits in a key to be hashed, and q be the number of bits desired in an output hash function. Choose a block size r ≤ p; the choice of block size controls the tradeoff between time and memory usage, so it should be made so that the tables are not too large, e.g., so that the tables fit into the computer's cache memory. [2]
2-left hashing—using two hash tables of equal size n/2, and asymmetrically resolving ties by putting the key in the left hash table—has fewer collisions and therefore better performance than 2-choice hashing with one large hash table of size n. [4] [full citation needed]