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Dynamic Perfect Hashing
Definition
Dynamic perfect hashing is defined as a programming method for resolving collisions in a hash table data structure.
Application
While more memory-intensive than its hash table counterparts, this method is ideal for situations where fast queries, insertions, and deletions must be performed on a large set of elements.
Implementation
Dietzfelbinger et al. explain a dynamic dictionary Algorithm that, when a set of m items is incrementally appended to the dictionary, membership queries always consume constant time and therefore O(1) worst-case time, the total storage needed is O(m) (linear), and O(1) expected amortized insertion and deletion time (amortized constant time).In the dynamic case, when a key is inserted into the hash table, if its entry in its respective sub table is occupied, then a collision is experienced and the sub table is rebuilt based on its new total entry count and randomly chosen hash function. Because the load factor of the second-level table is remained low, rebuilding is not frequent, and the amortized expected cost of insertions as well as amortized expected cost of deletions are O(1).
Additionally, the ultimate size of the top-level table or any of the sub tables has no prior knowledge in the dynamic case. One technique for maintaining expected O(m) space of the table is to prompt a full rebuilding when a sufficient number of insertions and deletions have experienced. As long as the total number of insertions or deletions exceeds the number of elements at the time of last construction, the amortized expected cost of insertion and deletion remain O(1) by considering full rehashing.
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