Double hashing

Definition

Double hashing is a collision resolution technique used in hash tables where a secondary hash function determines the step size for probing during collisions. When a key hashes to an already occupied slot, double hashing applies a second hash function to compute the new index, providing a way to find the next available slot. This method reduces clustering and offers a more uniform distribution of entries compared to linear or quadratic probing methods.

5 Must Know Facts For Your Next Test

1. Double hashing uses two different hash functions: one for computing the initial index and another to determine the step size when a collision occurs.
2. The second hash function in double hashing must be chosen carefully to ensure it produces values that are coprime with the table size, preventing infinite loops.
3. Double hashing is generally more efficient than other probing methods because it spreads out the keys more uniformly across the table.
4. It helps minimize clustering, which can degrade performance in linear and quadratic probing scenarios.
5. If the load factor of the hash table becomes too high, it can negatively impact the efficiency of double hashing, similar to other collision resolution methods.

Review Questions

• How does double hashing improve upon traditional collision resolution methods like linear probing?
  • Double hashing improves upon traditional methods like linear probing by using two distinct hash functions to determine the next available slot when a collision occurs. While linear probing simply checks subsequent slots sequentially, which can lead to clustering and reduced efficiency, double hashing introduces randomness in its search pattern. This results in a more uniform distribution of entries in the hash table, enhancing overall lookup performance and reducing the chances of long search sequences.
• What are the key considerations in choosing the second hash function for double hashing?
  • When selecting the second hash function for double hashing, it is critical that this function produces step sizes that are coprime with the size of the hash table. This ensures that all slots can eventually be probed if needed, preventing situations where certain slots become unreachable. The second hash function should also be computationally efficient to maintain the overall performance benefits of double hashing. A poorly chosen second function can negate the advantages gained by using double hashing.
• Evaluate how load factor affects the performance of double hashing and suggest potential solutions for maintaining efficiency in high-load scenarios.
  • The load factor significantly impacts the performance of double hashing; as it increases, the chances of collisions rise, leading to longer probe sequences and slower access times. To maintain efficiency in high-load scenarios, strategies such as resizing the hash table when a certain load factor threshold is reached can be employed. This involves creating a new larger table and rehashing existing entries. Additionally, employing dynamic resizing algorithms or increasing the capacity proactively can help manage load effectively and keep operations efficient.

Related terms

Hash Function: A mathematical function that converts an input (or 'key') into a fixed-size string of bytes, which is typically a hash code. It is crucial for the efficient retrieval of data in hash tables.

Collision: A situation that occurs in hash tables when two keys hash to the same index, requiring a strategy to resolve which key will occupy that position.

Probing: The method used to find an open slot in a hash table when collisions occur. This can involve techniques like linear probing, quadratic probing, or double hashing.