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We assume at least a two level tree here, ie, n > y 1 To nd the number of levels in the tree, we follow Eq 3-48 For y 1 an estimate for x is xest = logy n 4-11
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The exact height of the tree can be obtained by summing the number of records at the successive levels nlevel=x , nx 1 , , and stopping when all records are stored The expected, ie, average, fetch time can be computed by taking the fetch time for the nlevel records at each level and allocating this over the n records in the le The access path increases from 1 for level = x to x for the bottom level, and this accounts for the rst factor in the summation below
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The fetch time in a tree structure is varies by level, so that the average is not determined by the integer height of the tree, as were the indexes shown earlier Also, if the tree itself is used as an index, the pointers in the tree to the remote goal data can exist at various levels The smooth curve in Fig 4-11 is hence appropriate to describe the fetch time to fanout relationship seen here
Example 4-8
Hybrid File Organizations and
Comparison of performance of two tree-structured les similar B-tree indexed and indexed-sequential les
We will evaluate a tree-structured le and two alternative indexed les each for two cases, a short and b long records We will use similar parameters as were used in the example of a personnel le given as Example 3-9 of Sec 3-4 In case a we will assume that an employee goal record contains only a social security number of nine characters (VK ) and a skill code of six characters (VG ), so that R = 15; in case b we use a still modest record length of R = 180 characters The remaining parameters required are n = 20 000 records, B = 1 000 characters, P = 4 characters
Tree-structured le
For the tree-structured le we assume a dense packing of records, and use Eqs 4-9, 4-10, and 4-11 To verify that xest is indeed equal to x, we also present the contents of each level of the les Case a y = 1000 4 + 1 = 53 15+4 xest = log53 20 000 = 249 = 3 The les are then constructed as follows: Level Blocks Records Pointers 6 5 4 3 =x:1 52 53 2 53 2 756 2 809 1 331 17 192 Total 385 20 000 Hence TF =
1 52+2 2756+3 17192 (s 20 000
Case b y = 1000 4 + 1 = 6 180+4 xest = log6 20 000 = 521 = 6 Blocks Records Pointers =x:1 5 6 6 30 36 36 180 216 216 1 080 1 296 1 296 6 480 7 776 2 445 12 225 3 964 20 000
1 5+2 30++5 6480+6 12225 (s 20 000
+ r + btt)
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= 286 (s + r + btt)
= 553 (s + r + btt)
B-tree index to a data le
One of the alternatives to a tree-structured le is a le accessed via a B-tree index Here we can consider two further cases, one where the le is record-anchored, as required for multi-indexed les, and one where the le is block-anchored, which is adequate for indexedsequential les as vsam When the le is record anchored the record size does not a ect the fetch time, but in the block-anchored case the short records of case a require only n/Bfr = 20 000/ 1000/15 = 304 blocks and corresponding pointers, whereas the longer records require 20 000/ 1000/180 = 4000 pointers for the data blocks The fanout in the index is determined by the density and the entry size VK + P = 13 Record-anchored Cases a and b y = 069 1000 = 52 13 x = log52 20 000 = 251 = 3 Fetching a record requires one more access to the le; hence TF = (x + 1)(s + r + btt)=4(s + r + btt) Block-anchored Case a Case b also y = 52 y = 52 x = log52 304 = 2 x = log52 4 000 = 3
3(s + r + btt)
4(s + r + btt)
Sec 4-4 3
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