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5.4. QUERY PROCESSING 93
particular there are only 41 different values for the year element of the books.
The selectivity of 1.0 for the /dblp/article/year path expression indicates that all
values are the same. The selectivity for the other elements that have values in
this DBLP fragment can be seen in the figure.
The values r and sl are used when estimating the number of elements that correspond
to a path expression to be evaluated. This number is the result of a
multiplication of all r values on the path to the selected element. If the path
expression contains a key comparison the value for its selectivity is multiplied
additionally.
Example 14 The path expression /dblp/article/author will lead to 1 · 535 · 1.69 = 904
selected elements.
The same path expressions with a value comparison (/dblp/article/author[. = ′ x ′ ])
leads to 904·0.621 = 561 selected elements. This number is relatively high because
the 535 articles in the selected DBLP fragment are written by only 342 different authors.
The similar path expression /dblp/article/title[. = ′ x ′ ] leads to only 1 · 535 · 1 ·
0.002 = 1.07 hits. Therefore, querying an article by its title is more than 300
times faster than querying it by the authors.
If the query contains a wildcard (*) or the descendant axis (//) multiple extents
must be regarded. The values for r can be summarized in order to get the final
result. With a key in the path expression the r values of the different affected
extents have to be weighted by the selectivity sl before summarizing them.
Example 15 The path expression /dblp/ ∗ /url affects three url extents of books,
articles and inproceedings. We calculate their numbers independently and summarize
them afterwards. Therefore, the result of this path expression has the
expected cardinality 1 · 540 · 0.18 + 1 · 535 · 0.04 + 1 · 26565 · 1.0 = 26684.
The statistic DataGuide is a relatively simple but in most cases sufficient and
efficient approach to estimate the cardinality of selected elements of a path expression.
The particular value can be used in cost models for indexes and conventional
XPath evaluation.
The approach assumes statistical independence between elements in the XML
data. If we have elements that are statistically dependent, for instance they are
mutually exclusive the statistic DataGuide will lead to reduced precision: For
instance, an element X has two children a and b. Half of the X elements have
exactly one a child and the other half has exactly one b child. Therefore, no X element
has both an a and b child. The statistic DataGuide would assign r = 0.5 for
the a and b extent. The path expression //X[a and b] would lead to an estimated
cardinality of |X| · 0.5 · 0.5 = |x|
4
indicating that a quarter of the X elements have
both an a and b value.