Double hashing

Definition

Double hashing is a collision resolution technique used in hash tables, where a secondary hash function is applied to resolve collisions more effectively. This method enhances the distribution of keys and minimizes clustering by using two different hash functions to calculate a probe sequence. When a collision occurs, the second hash function generates an offset that allows the algorithm to search for the next available slot in the hash table.

5 Must Know Facts For Your Next Test

1. Double hashing employs two hash functions: the first one determines the initial index, while the second one calculates the step size for resolving collisions.
2. The step size in double hashing is crucial, as it must be relatively prime to the size of the hash table to ensure all slots can be probed effectively.
3. Compared to linear probing or quadratic probing, double hashing tends to produce a more uniform distribution of keys and reduces clustering issues.
4. Performance of double hashing depends on how well the hash functions are designed; poorly chosen functions can lead to inefficient probing and longer search times.
5. In practice, double hashing can be more computationally intensive due to the need for two hash calculations for each insertion and retrieval operation.

Review Questions

• How does double hashing differ from other collision resolution techniques like linear and quadratic probing?
  • Double hashing differs from linear and quadratic probing by using two distinct hash functions instead of a single fixed interval. In linear probing, subsequent slots are checked sequentially, which can lead to clustering, while quadratic probing uses a squared increment that also suffers from clustering. Double hashing minimizes clustering by generating an offset with its second hash function, allowing for a more randomized probe sequence that increases efficiency in finding empty slots.
• Discuss the importance of choosing appropriate hash functions in double hashing and its impact on performance.
  • Choosing appropriate hash functions in double hashing is critical for ensuring optimal performance. The primary hash function should distribute keys uniformly across the table, while the secondary function must be designed such that its output is relatively prime to the table size. This ensures that all slots can be probed without creating repetitive cycles, which can significantly affect lookup times and increase the likelihood of successful insertions. Poorly designed hash functions can lead to longer search times due to inefficient probing sequences.
• Evaluate how double hashing impacts memory utilization in hash tables compared to other collision resolution methods.
  • Double hashing positively impacts memory utilization in hash tables by reducing clustering and allowing for more efficient use of available slots. Unlike linear or quadratic probing, where collisions can lead to contiguous filled slots and wasted space, double hashing spreads out entries more evenly across the table. This results in fewer empty slots within a loaded table and enhances performance by decreasing average search times for insertions and lookups. Ultimately, this leads to a more compact use of memory resources while maintaining high performance.

Related terms

hash function:

A mathematical algorithm that transforms input data into a fixed-size string of characters, which typically represents the original data uniquely.

collision resolution:

A method used to handle situations when two keys hash to the same index in a hash table.

open addressing:

A collision resolution strategy where all entries are stored in the hash table itself and probing is used to find available slots.