External hasing with limited internal storage

The following problem is studied: How, and to what extent, can the retrieval speed of external hashing be improved by storing a small amount of extra information in internal storage? Several algorithms that guarantee retrieval in one access are developed and analyzed. In the first part of the paper, a restricted class of algorithms is studied, and a lower bound on the amount of extra storage is derived. An algorithm that achieves this bound, up to a constant difference, is also given. In the second part of the paper a number of restrictions are relaxed and several more practical algorithms are developed and analyzed. The last one, in particular, is very simple and efficient, allowing retrieval in one access using only a fixed number of bits of extra internal storage per bucket. The amount of extra internal storage depends on several factors, but it is typically very small: only a fraction of a bit per record stored. The cost of inserting a record is also analyzed and found to be low. Taking all factors into account, this algorithm is highly competitive for applications requiring very fast retrieval.