Section 4 - Bucket Hashing
Closed hashing stores all records directly in the hash table. Each record R with key value kR has a home position that is h(kR), the slot computed by the hash function. If R is to be inserted and another record already occupies R's home position, then R will be stored at some other slot in the table. It is the business of the collision resolution policy to determine which slot that will be. Naturally, the same policy must be followed during search as during insertion, so that any record not found in its home position can be recovered by repeating the collision resolution process.
One implementation for closed hashing groups hash table slots into buckets. The M slots of the hash table are divided into B buckets, with each bucket consisting of M/B slots. The hash function assigns each record to the first slot within one of the buckets. If this slot is already occupied, then the bucket slots are searched sequentially until an open slot is found. If a bucket is entirely full, then the record is stored in an overflow bucket of infinite capacity at the end of the table. All buckets share the same overflow bucket. A good implementation will use a hash function that distributes the records evenly among the buckets so that as few records as possible go into the overflow bucket.
When searching for a record, the first step is to hash the key to determine which bucket should contain the record. The records in this bucket are then searched. If the desired key value is not found and the bucket still has free slots, then the search is complete. If the bucket is full, then it is possible that the desired record is stored in the overflow bucket. In this case, the overflow bucket must be searched until the record is found or all records in the overflow bucket have been checked. If many records are in the overflow bucket, this will be an expensive process.
This applet will demonstrate bucket hashing as described above. Try inserting several records, forcing some into the overflow bucket.
A simple variation on bucket hashing is to hash a key value to some slot in the hash table as though bucketing were not being used. If the home position is full, then the collision resolution process is to move down through the table toward the end of the bucket while searching for a free slot in which to store the record. If the bottom of the bucket is reached, then the collision resolution routine wraps around to the top of the bucket to continue the search for an open slot. For example, assume that buckets contain eight records, with the first bucket consisting of slots 0 through 7. If a record is hashed to slot 5, the collision resolution process will attempt to insert the record into the table in the order 5, 6, 7, 0, 1, 2, 3, and finally 4. If all slots in this bucket are full, then the record is assigned to the overflow bucket. The advantage of this approach is that initial collisions are reduced, Because any slot can be a home position rather than just the first slot in the bucket.
This applet will demonstrate the variation on bucket hashing. Try inserting several records, forcing some into the overflow bucket. Try to determine why this variation will improve performance over the first version of bucket hashing. Also, think about why bucket hashing in general should improve performance over open hashing when the hash table is stored on disk.
Bucket methods are good for implementing hash tables stored on disk, because the bucket size can be set to the size of a disk block. Whenever search or insertion occurs, the entire bucket is read into memory. Because the entire bucket is then in memory, processing an insert or search operation requires only one disk access, unless the bucket is full. If the bucket is full, then the overflow bucket must be retrieved from disk as well. Naturally, overflow should be kept small to minimize unnecessary disk accesses.