Cuckoo hashing
Introduction
Cuckoo hashing is a computer science algorithm for resolving hash collisions in a hash table. This algorithm was first proposed by Rasmus Pagh and Flemming Friche Rodler in 2001. It is named after the behavior of the cuckoo bird, which lays its eggs in other birds' nests, pushing out the existing eggs in the process.
Overview
Cuckoo hashing is a scheme in computer science used for resolving hash collisions in a hash table. Hash collisions occur when two different keys produce the same hash value. In cuckoo hashing, each key is assigned two possible positions in the hash table, calculated by two different hash functions. If a new key is inserted into a position that is already occupied, the existing key is displaced to its alternative position. This process is repeated until all keys have a position in the hash table, or until a predefined number of displacements have been made.
Hash Functions
In cuckoo hashing, two hash functions are used to determine the possible positions for a key in the hash table. The hash functions must be independent and uniformly distributed to ensure that each key has an equal chance of being placed in any position in the hash table. The choice of hash functions can significantly impact the performance of cuckoo hashing. If the hash functions are not well-chosen, the algorithm may enter an infinite loop, continually displacing keys without ever finding a suitable position for all keys.
Insertion Process
The insertion process in cuckoo hashing involves several steps. First, the two potential positions for the new key in the hash table are calculated using the hash functions. If either of these positions is empty, the key is inserted into that position. If both positions are occupied, the key is inserted into one of the positions, displacing the key that was previously in that position. The displaced key is then reinserted into its alternative position, displacing any key that was there, and so on. This process continues until a position is found for every key, or until a predefined limit on the number of displacements is reached.
Performance
The performance of cuckoo hashing depends on several factors, including the load factor of the hash table, the quality of the hash functions, and the limit on the number of displacements. Under ideal conditions, cuckoo hashing can achieve a worst-case lookup time of O(1), which is significantly better than most other collision resolution schemes. However, the worst-case insertion time can be O(n), which occurs when the algorithm enters an infinite loop of displacements. To prevent this, a limit is typically set on the number of displacements, after which the hash table is resized or rehashed.
Applications
Cuckoo hashing is used in various applications in computer science, including databases, caches, and routers. It is particularly useful in situations where fast lookup times are critical, and where the set of keys is relatively static, as the insertion process can be time-consuming.