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Table 3-4 shows some attributes and their likely distribution of values Then we show for each attribute a sample value expression for a query, and the estimated percentage of the le retrieved using the assumption of a uniform distribution, followed by the actual value, obtained from an experiment using real data

5

namespace Example_15_7_ _ _ _Splitting_Strings { class Tester { public void Run( ) { // create some strings to work with string s1 = "One,Two,Three Liberty Associates, Inc."; // constants for the space and comma characters const char Space = ' '; const char Comma = ','; // array of delimiters to split the sentence with char[] delimiters = new char[] { Space, Comma }; int ctr = 1; // split the string and then iterate over the // resulting array of strings String[] resultArray = s1.Split(delimiters); foreach (String subString in resultArray) { Console.WriteLine(ctr++ + ":" + subString); } } static void Main( ) { Tester t = new Tester( ); t.Run( ); } } }

Range or cardinality Type of Query distribution Zipf normal Erlang(2) uniform Estimate of Result 5% 20% 125% 5% Actual Result 13% 3% 42% 45%

The output looks like this:

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The estimate can be improved if for each attribute additional information is kept For small value sets the actual counts may be kept Counts would provide exact values for the Style, Bedrooms, and Location attributes Keeping, instead of the range, ten decile boundaries of the value distribution permits a more precise estimation of continuous values, as Price above A better scheme is to maintain distribution steps, where the partitions have equal sizes Distribution information tends to be associated with indexes, and is best updated as the indexes are When only a few parameters are kept to describe the distribution, we can expect to nd the information in the root block and rapidly retrieved The values in the root block provide already an initial estimation of the distribution steps, since in the sizes of the subtrees for each entry will be similar For instance, given that the root block of the Price index has 100 entries we would nd that the value = 212K will appear in entry 97 or 98, giving a much more accurate estimate of the selectivity than that provided by the assumption of uniform distribution All these techniques still ignore the correlation of values In WuthHeights the dominant Style may be Greek Revival and the Prices always above $150 000 The storage and update demands for such second-order information make its retention impractical

Example 15-7 starts by creating a string to parse:

An Index Structure for Dynamic Updating B-trees In indexed les every change of an indexed attribute will require the insertion, deletion, or both, of an index entry into the appropriate index block To make such changes feasible, we reduce the density of the index Extra space is left initially empty in each index block, and now one insertion will a ect only that index block The blocks can accommodate a number of insertions, and only when the block is lled is another block obtained Half the entries from the full block are distributed to the new block There has been a trade-o made here: space has been given up to have reasonable maintenance of the index A method based on this solution is the B-tree, and we will describe a speci c version of this algorithm useful for index trees A B-tree has index blocks which are

string s1 = "One,Two,Three Liberty Associates, Inc.";

Sec 3-4

The delimiters are set to the space and comma characters. Then call Split( ) on the string, passing in the delimiters:

.

kept at least half full; the e ective fanout yeff is hence between y and y/2 as shown in Fig 3-15 B-trees and Index B-trees The original B-tree was de ned with space in each block for y pointers and y 1 values In a block of an index B-tree, however, up to y values are kept, and the value (v1 ) appears redundantly, as shown in Fig 5-14 The value in the rst entry (v1 ) is the same as the value (vn ) in the entry referring to this block in the next-higher-level index block This redundancy is avoided in pure B-trees The index B-tree approach makes the entries consistent in format, permits index blocks to be accessed independently of their ancestor blocks, and has little e ect on the analyses when y is reasonably large y = ymax = 8, yinitial = y/2 = 4, yeff = 6 vn pn v1 p1

String[] resultArray = s1.Split(delimiters);

Figure 3-15

Split( ) returns an array of the substrings that you can then iterate over using the foreach loop, as explained in 10:

foreach (String subString in resultArray)

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