NONOBLIVIOUS HASHING

Nonoblivious hashing, where information gathered from unsuccessful probes is used to modify subsequent probe strategy, is introduced and used to obtain the following results for static lookup on full tables: (1) An O(1)-time worst-case scheme that uses only logarithmic additional memory, (and no memory when the domain size is linear in the table size), which improves upon previously linear space requirements. (2) An almost sure O(1)-time probabilistic worst-case scheme, which uses no additional memory and which improves upon previously logarithmic time requirements. (3) Enhancements to hashing: (1) and (2) are solved for multikey records, where search can be performed under any key in time O(1); these schemes also permit properties, such as nearest neighbor and rank, to be determined in logarithmic time.