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TF o = o
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1 R R = o t 2 t
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over ow 3-16
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as the term needed to process changes made to the main le We cannot expect that the simple systems which use sequential les will search through both the main le and the log le in parallel The total fetch time, if both parts of the le are searched sequentially, is the sum TF = R 1 (n + o) 2 t 3-17
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where o is the capacity of the transaction log le
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A well-known search technique for memory can be adapted to provide an alternate access method for sequential les The binary search begins, as shown in Fig 3-5, with a direct access to the middle of the le, and partitions the le iteratively according to a comparision of the key value found and the search argument Whenever a block is fetched, the rst and last records in this block will be inspected to determine if the goal record is within this block The number of fetches does not depend on the number of records, n, but rather on the number of blocks, b = n/Bfr We nd, using the expected number of block access for the binary search log2 (b) (Knuth73S ), that
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TF = log2
n Bfr
(s + r + btt + c) + TF o
binary 3-18
Sec 3-2
The Sequential File
The term for processing time, c, is included here, since until the record range in a block has been checked, it is not known which block is to be read next The e ciencies obtained when reading the le sequentially using alternate bu ers have been lost in this case The value of c may well be negligible compared with the other times involved, but the bulk transfer rate, t , is always inappropriate The over ow term remains unchanged A third access method for sequential les, probing, is more di cult to quantify It consists of an initial direct fetch, or probe, to an estimated position in the le, followed by a sequential search If only forward sequential searches can be executed e ciently, the initial probe will be made to an estimated lowest matching key position, so that having to read backward is rare Only one seek is made, and the number of blocks read sequentially is based on the uncertainty of the probe Likely values for an initial probe have been based on the leading digits of a social security number, if its value is used as a key, or on a percentile expectation for leading characters of names, if names are the key Names beginning with the letters E , for instance, may be found after 02446n records in a le sequenced by name (see Table 14-5) The corresponding block would be numbered 02446n/Bfr There is some uncertainty in the distribution leading to a probe Since on most devices a forward search is best, one can decide, given a 3% or 003 uncertainty, that the probe may actually best begin at the block numbered 02146n/Bfr and search forward Alternate techniques to access records rapidly are used by the indexed and direct le organization methods described in subsequent chapters
Probing Summary of Access Methods We can summarize the three choices of access methods as follows 1 Sequential search: O(n) 2 Binary search: O(log n) 3 Probing: O(1) While the big-O notation clearly distinguishes the di erence in growth patterns for these three alternatives, it ignores the complexity of the programs and the important factors of block access and key distribution For many modestly-sized les the simple sequential search may remain preferable Only when the les are quite large are the more complex access methods warranted The simpler methods are also more susceptible to hardware improvements, as described in the section on database machines, Chap 2-5
In a sequential le, a successor record is immediately accessible and may well be in the same block If there is a frequent need for successor records, the le system should be programmed so that it does not discard the remaining records in the block but keeps the bu er with the contents of the current block available The probability of nding a successor record in the same block is determined by the number of records per block Bfr : in 1/Bfr of the cases the next block is required If the processing speed satis es the condition of Eq 2-22, the expected time to get the next record is only
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