Hopscotch hashing

Hopscotch hashing is a scheme in computer programming for resolving hash collisions of values of hash functions in a table using open addressing. It is also well suited for implementing a concurrent hash table. Hopscotch hashing was introduced by Maurice Herlihy, Nir Shavit and Moran Tzafrir in 2008. The name is derived from the sequence of hops that characterize the table's insertion algorithm.

The algorithm uses a single array of n buckets. For each bucket, its neighborhood is a small collection of nearby consecutive buckets (i.e. ones with close indices to the original hashed bucket). The desired property of the neighborhood is that the cost of finding an item in the buckets of the neighborhood is close to the cost of finding it in the bucket itself (for example, by having buckets in the neighborhood fall within the same cache line). The size of the neighborhood must be sufficient to accommodate a logarithmic number of items in the worst case (i.e. it must accommodate log(n) items), but only a constant number on average. If some bucket's neighborhood is filled, the table is resized.

In hopscotch hashing, as in cuckoo hashing, and unlike in linear probing, a given item will always be inserted-into and found-in the neighborhood of its hashed bucket. In other words, it will always be found either in its original hashed array entry, or in one of the next H-1 neighboring entries. H could, for example, be 32, a common machine word size. The neighborhood is thus a "virtual" bucket that has fixed size and overlaps with the next H-1 buckets. To speed the search, each bucket (array entry) includes a "hop-information" word, an H-bit bitmap that indicates which of the next H-1 entries contain items that hashed to the current entry's virtual bucket. In this way, an item can be found quickly by looking at the word to see which entries belong to the bucket, and then scanning through the constant number of entries (most modern processors support special bit manipulation operations that make the lookup in the "hop-information" bitmap very fast).

Here is how to add item x which was hashed to bucket i:

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