Optimality in External Memory Hashing

Hash tables on external memory are commonly used for indexing in database management systems. In this paper we present an algorithm that, in an asymptotic sense, achieves the best possible I/O and space complexities. Let B denote the number of records that fit in a block, and let N denote the total number of records. Our hash table uses 1+𝑂(1/√B) I/Os, expected, for looking up a record (no matter if it is present or not). To insert, delete or change a record that has just been looked up requires 1+𝑂(1/√B) I/Os, amortized expected, including I/Os for reorganizing the hash table when the size of the database changes. The expected external space usage is 1+𝑂(1/√B) times the optimum of N/B blocks, and just O(1) blocks of internal memory are needed.