Bucketing

Bucketing makes the hash table a 2D array instead of a single dimensional array. Every entry in the array is big enough to hold N items (N is not amount of data. Just a constant).

Problems:

• Lots of wasted space.
• If N is exceeded, another strategy will need to be used
• Not good for memory based implementations but doable if buckets are disk-based)

For bucketing it is alright to have $\lambda > 1$. However, the higher $\lambda$ is the higher a chance of collision. $\lambda > 1$ guarantees there will be at least 1 collision (pigeon hole principle). That will increase both the run time and the possibility of running out of buckets.

For a hash table of N locations and X buckets at each location:

• Successful Search - O(X) worst case
• Unsuccessful Search - O(X) worst case
• Insertion - O(X) - assuming success, bucketing does not have good way to handle non-successful insertions.
• Deletion - O(X)
• Storage: O(N * X)