url - Universität zu Lübeck

6.3. INDEX SELECTION PROBLEM APPLIED TO KEYX INDEXES 109
Definition 22 (Index Candidates)
The index candidates are defined as a function ican : P → P(D) returning a set
containing all possible index declarations for a given path expression p. The following
definition combines and permutes the key nodes:
ican(p) = {([k 1 , k 2 , . . . , k m ], value(p)) | k j ∈ key(p) ∧
In total we have to consider ∑ m
n=0
1 ≤ j ≤ m ∧ 1 ≤ m ≤ |key(p)|}
m!
(m−n)!
− 1 different possible indexes. As most of
these indexes are dropped during ISP calculation, we call them index candidates
of the path expression p. Index candidates are virtual and not materialized in the
database.
Example 16 A query o with the path expression
p 5 = /dblp/article[author = ”X” and title = ”Y ”]
has the following key and value nodes:
key(p 5 ) = {/dlbp/article/author, /dlpb/article/title}
value(p 5 ) = /dlbp/article
All index candidates are listed below. As the order of key nodes matters, the first
two index candidates of ican(p 5 ) are not equivalent.
ican(p 5 ) = {i 1 p 5
, i 2 p 5
, i 3 p 5
, i 4 p 5
} with
i 1 p 5
= ([/dblp/article/author, /dblp/article/title], /dblp/article)
i 2 p 5
= ([/dblp/article/title, /dblp/article/author], /dblp/article)
i 3 p 5
= ([/dblp/article/author], /dblp/article)
i 4 p 5
= ([/dblp/article/title], /dblp/article)
The two multi-key indexes i 1 p 5
and i 2 p 5
constitute the best suitable indexes for p 5
as they reflect both key nodes. In contrast the two indexes i 3 p 5
and i 4 p 5
require
additional processing of the referenced nodes, but are still more efficient than an
evaluation of the plain path expression without an index. Please notice that the
number of index candidates grows exponentially with the number of key nodes
of a path expression and increases the costs of solving the ISP dramatically. A
path expression with 4 key nodes will lead to 64 index candidates! Heuristics to
decrease the computational expense have to start at this point by reducing the
number of index candidates.
To consider the whole workload we need to regard the index candidates of all
database operations o ∈ W . This is done by unifying the index candidates of all
operations to the total index candidate set.