The Spatial Complexity of Oblivious K Probe Hash Functions

Jeanette Schmidt

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Altogether, we need at most [lognj-l-l different ki values, where ki is the i"" multiplier servicing about 1/2' of the buckets. Moreover, the information content of the map from bucket indices into these [log nj -f 1 multipliers (i. E. , the representation of the table A' with Huffman coding) is 0(ri).
In summary, the optimal perfect hash function is that described above, with two modifications: 1. The (uncompressed) hash value is /i, (i-) = ((kiX mod p) mod 2c?) + 2C, -.
2. The multiplier valu...es k are iteratively selected to satisfy the one-to-one requirement of the maximum number of (unsatisfied) hi's.
It remains to show how to achieve a compact encoding of the content of the tables A', C, and D to require only 0{n) bits, that is readily decodable in 0(1) time in our computational model. The basic decoding operations we will use are as follows: 1. Extract a subsequence of bits from one word.
2. Concatenate two bit strings of altogether O(logn) bits.
10 3. Locate the bit-index of the ^--th zero in a word.

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