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Cylinder over ow areas The cost of over ows out of the main le can be lowered again by allocating over ow areas on each cylinder This requires modi cation of the key-to-address transformation to account for the gaps in the primary addressing space If buckets are already used, it may be better to use this space to reduce the density per bucket Linkage to Colliding Records Once the block for an over ow is located, the record is yet to be found Over ow records in successor blocks can be found either by simply matching all successive records in the block to the search argument, or by maintaining a chain to link the over ow records together Without a chain the search for a record or for a free slot for an insertion terminates when an empty slot is reached This approach constrains the deletion of records, as discussed below In a densely loaded le it may take many accesses to nd an empty slot, because many intervening slots may be lled by records belonging to the set associated with a di erent primary bucket address To identify
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an arbitrary stored record as a member of the set of colliding records for a speci c prime bucket, the key of the stored record accessed has to be transformed to the corresponding address, which is then matched to the initial bucket address If the addresses are equal, this record belongs to this collision set The use of a pointer chain avoids accessing records which do not have the same computed bucket address Now fetches can be limited to the set of colliding records The use of the chain also improves fetches where the record is not in the le, since the search terminates when the chain pointer is , rather than going on to a free slot For insertions it is best to use any free slot in the nearest bucket If chains are used, the inserted record must be linked into the chain The linkage of records into the chain at the current block improves locality This is probably more e ective than trying to keep records in sequential order by key or by access frequency
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DELETION FROM DIRECT FILES Deletion of a record involves some additional considerations We have to assure that the freed slot does not hinder subsequent fetch usage, and we also would like to have the slot available for reuse to avoid excessive reorganizations
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We will rst consider the cases where a chain is used to link the records of a collision set The use of a chain requires that deletions mark the slot Empty and also that the chain is reset so that any successor records can still be retrieved If there is more than one record in the collision set, the predecessor record has to be rewritten with the pointer value from the deleted record Subsequent insertions should use free slots close to the primary bucket, so that the search path does not become longer and longer Open addressing methods can be used without a chain In that case a search for a record to be fetched or for a free slot for an insertion terminates when an empty slot is reached This means that deleted records cannot just have their slot set to Empty, but we have to adjust the le to avoid breaking a subsequent search Either a tombstone has to be set, which indicates that this record, although deleted, is still on the path to successor over ow records, or the last record of the collision set has to be moved to ll this freed slot In this latter case the slot can still not be marked Empty, because it may be traversed by some other collision set Its tombstone, however, can indicate Deleted, and show that the slot is available for reuse Dealing with Clusters Figure 3-22 illustrates what can happen in these clusters of collision sets when we use open addressing, no chains, and sequential search for slots for over ows Some deleted record spaces can be reused, but the path length for fetches and inserts includes all spaces not explicitly marked empty After many deletions and insertions there will be many slots which hold markers and no data This increases the number of slots to be scanned when searching The e ective density of the le is hence greater than n/m, and this can considerably reduce the performance of a direct le The performance can be recovered during reorganization Breaking clusters can be performed incrementally, on a block by block basis During such a reorganization it is possible to collect su cient information about the collisions to either or both 1 reset deleted slots which are not within any collision set to Empty to break clusters no longer needed 2 rearrange the records in any clusters to optimize access A complete reorganization would rehash all the keys in the block and place the records in order by computed address
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3-5-2 Use of Direct les Hashed random access is an invention speci c to computers and has been used to access data on the earliest disk les Direct les nd frequent use for directories, pricing tables, schedules, name lists, and so forth In such applications where the record sizes are small and xed, where fast access is essential, and where the data is always simply accessed, the direct le organization is uniquely suitable Simple access here means use of a single key for retrieval, and no serial access Hashing is not appropriate for attributes which have a poor selectivity The clusters in the source key are reserved when hashing, and may coalesce with other clusters Managing deletion in clusters is costly as well
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