Algebra-based identification of tree patterns in ... - Semantic Scholar

Algebra-based identification of tree patterns in XQuery 
   
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INRIA Futurs, Gemo group, France [email protected] 2 LRI, Univ. Paris 11, France [email protected] 3 CSE Dept., UCSD, USA [email protected] 4 IIT Bombay, India [email protected]

Abstract. Query processing performance in XML databases can be greatly enhanced by the usage of materialized views whose content has been stored in the database. This requires a method for identifying query subexpressions matching the views, a process known as view-based query rewriting. This process is quite complex for relational databases, and all the more daunting on XML databases. Current XML materialized view proposals are based on tree patterns, since query navigation is conceptually close to such patterns. However, the existing algorithms for extracting tree patterns from XQuery do not detect patterns across nested query blocks. Thus, complex, useful tree pattern views may be missed by the rewriting algorithm. We present a novel tree pattern extraction algorithm from XQuery queries, able to identify larger patterns than previous methods. Our algorithm has been implemented in an XML database prototype [5]. We study its performance, and the overall benefits of our tree pattern identification approch.

1

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def

f ull($x q) = f ull(q$x) BCe1 .ID ≺ e2 .ID (f ull(q))

Y 6 -  $W, 6   & - $+j

>,. 
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>,. ret(q$x ) e2 .ID , 6 9,. +P D P++# 4
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= $x b p$z = $y e



p$t = $z f _ 

f ull(p$x) = ea BCe .ID≺e.ID e f ull(p$y ) = eb f ull(p$z ) = f ull(p$y ) BCe .ID≺≺ e .ID ed a

$y




1 Y

d

f ull(p$t ) = f ull(p$z ) BCe$z .ID≺≺ ef .ID ef

& 
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$ p1 = $x//c p2 = $y//e

 # $'p,.&%,'BLM?T , 6 Z;4K
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p4 = $t//h

.ID≺ ≺ e .ID ec

p3 = $t[g/text() = 5] 

f ull(p1) = f ull(p$x) BCe$x f ull(p2) = f ull(p$y ) BCe$y .ID≺≺ ee .ID ee c f ull(p3) = f ull(p$t) BB,'N, 6 .,.-
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def



alg(hti{q}h ti) = xml(n(alg(q)),htiA1 h ti)

for $x1 in p1 , $x2 in $x1 /p2 ,. . . , $xk in $x1 /pk xq1 where $x1 /pk+1 θ $x1 /pk+2 and . . . $x1 /pm−1 θ $x1 /pm return $x1 /pm+1 , $x1 /pm+2 , . . . , $x1 /pn def

f ull(xq1 ) = σAk+1 θ Ak+2 ,...,Am−1 θ Am (f ull(p1 )BCID1 ≺ID2 f ull(//p2 ) . . . BCID1 ≺IDk f ull(//pk ) n BCn Cn ID1 ≺IDk+1 f ull(//pk+1 )B ID1 ≺IDk+2 . . . BCID1 ≺IDm f ull(//pm ) n n BCID1 ≺IDm+1 f ull(//pm+1 )BCID1 ≺IDm+2 . . . BCn ID1 ≺IDn f ull(//pn ) ) def

alg(xq1 ) = πAm+1 ,Am+2 ,...,An (f ull(xq1 )) Fig. 3. Generic XQuery query with simple return expression.

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++# 4
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xq4

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Fig. 5. Sample query performance measure.




#  
>

(∗) f ull(q) = f ull(p$x) × f ull(p$y ) BC@ne$x .ID=e$x .ID f ull(p1) BC@ne$y .ID=e$y .ID f ull(p2)BC@ne$y .ID=e$y .ID f ull(q2) q


$G,''
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alg(q) = xmltempl (f ull(q))

Y 6 -

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xmltempl 

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f ull(q)



σ(e$z .ID6=⊥)∨(e$z .ID=⊥∧e2 =⊥) ( f ull(p$x) BC@ne$x .ID≺≺ ec .ID ec × f ull(p$y ) BC@ne$y .ID≺≺ ee .ID ee BC@ne$y .ID≺≺ ed .ID (ed BC@ned .ID≺≺ ef .ID (ef BCnef .ID≺≺ eg .ID σV =5 (eg )BC@ned .ID≺≺ eh .ID eh )))

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V11



alg(q) = xmltempl (σ(e$z .ID6=⊥)∨(e$z .ID=⊥∧e2 =⊥) (V10 × V11 ))

576 

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