Classical Applied Data Structure
Double hashing with open addressing is a classical data structure on a table . Let be the number of elements stored in then 's load factor is .
Double hashing approximates uniform open address hashing. That is, start by randomly, uniformly and independently selecting two universal hash functions and to build a double hashing table .
All elements are put in by double hashing using and . Given a key, determining the -st hash location is computed by:
Let have fixed load factor . Bradford and Katehakis showed the expected number of probes for an unsuccessful search in, still using these initially chosen hash functions, is regardless of the distribution of the inputs.
Previous results include: Guibas and Szemerédi showed holds for unsuccessful search for load factors . Also, Lueker and Molodowitch showed this held assuming ideal randomized functions. Schmidt and Siegel showed this with more realistic -wise independent and uniform functions (for, and suitable constant ).
Like linear probing, it uses one hash value as a starting point and then repeatedly steps forward an interval until the desired value is located, an empty location is reached, or the entire table has been searched; but this interval is decided using a second, independent hash function (hence the name double hashing). Unlike linear probing and quadratic probing, the interval depends on the data, so that even values mapping to the same location have different bucket sequences; this minimizes repeated collisions and the effects of clustering. In other words, given independent hash functions and, the jth location in the bucket sequence for value k in a hash table is:
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