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the cost of over ows from collisions can be greatly reduced by grouping of the slots into buckets A typical bucket is equal to one block, as shown in Fig 3-21 A search through all the slots in the bucket is used to locate space for the new record Only computational time is required to access the records within a bucket Only when the bucket itself is lled will a disk access be needed The cost of the disk access depends on which of the three alternative over ow methods, shown next, is in use If the bucket contains y slots there will be space for ovpb collisions within the block, where ovpb = 1 n m y 3-69
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namely, the fraction of free space times the number of slots We can use the blocking factor Bfr for y if we are careful to remember that we are talking here about slots, and not records The cost of most collisions is now drastically reduced An analysis of the e ect of the use of buckets is unfortunately quite complex Figure 3-23 gives results for the use of buckets with a linear search in the le We nd for the earlier example (n/m = 069) and Bfr = 8 a reduction in collision cost from 35% to 5%, as marked with an x in Fig 3-23 Bucket Addresses When buckets are used, the entire block is made available when a record is required Now a shorter address can be used If there are y slots in a bucket, the address space reduces from m to m/y and the size of an address pointer will be log2 y bits less We now consider methods to resolve collisions
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When an over ow out of the bucket does occur, the search can continue to the next sequential block This avoids the costs of seek times to new areas but tends to cluster over ows together The linear search method for over ow slots is predominant for direct les, since it is simple and, one hopes, infrequently invoked As long as the number of entries is less than the number of slots available (n < m), a record space will eventually be found Since the availability of a free slot can be determined a priori, no alternate termination method is required The problem of clustering is that, when an area of the storage space is densely used, fetches need many search steps Additional insertions tend to increase the size of the dense area disproportionally Clustering has been shown to be quite detrimental even for moderately loaded direct les; an example of how clusters develop is shown in Fig 3-22 To avoid the clusters one may assign the bucket for the over ow at a random position in the le A new randomizing key-to-address computation computes a new slot address in the same le space Rerandomization, when applied to storage devices, causes a high overhead, since generally a new seek is required Further collisions can occur, and the procedure may have to be repeated A randomizing procedure cannot easily guarantee that it will ever locate an empty space Rerandomization techniques commonly are used when hashing in primary memory, but for les they appear less bene cial They probably should also be evaluated carefully when it appears that memory is used, but the operating system uses paging for virtual memory management
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The third method of handling collisions is to put all records which cause a bucket over ow into a separate le with a linkage from the primary record, similar to the over ow chains used in indexed-sequential les If such a separate over ow area is established, no clustering will take place An over ow still causes a new seek but avoids the repeated block fetches which can occur with the previous two methods A di culty here lies in the allocation of su cient over ow space, since the number of collisions is not absolutely predictable The over ow area may ll while the main area has much free space
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