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XML Query Processing
CPS 216
Advanced Database Systems
2
Announcements (March 31)
Course project milestone 2 due today
Hardcopy in class or otherwise email please
I will be out of town next week
No class on Tuesday (April 5); will make up during reading period Badrish Chandramouli will give the lecture on Thursday (April 7)
Homework #3 in less than two weeks (April 12)
Reading assignment for next week will be assigned
through email
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Overview
Recall that XML queries based on path expressions
can be expressed by joins
Node/edge-based representation (graphs)
Equi-join on id ’s Chasing pointers ≈ index nested-loop joins )“Navigational” approach
Interval-based representation (trees)
“Containment” joins involving left and right Sort-merge joins, zig-zag joins with indexes )“Structural” approach
Navigational processing in Lore
VLDB 1999
Lore data model peculiarity: labels on edges instead of labels on nodes Access paths in Lore Base representation: (parent, label) → child Label index: (child, label) → parent Edge index: label → (parent, child) Value index: (value, label) → node Path index: path expression → node
Correspond to the following in a label-on-node model label/value → node (parent, label) → child child → parent
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Navigational plans in Lore
//A/B/C[.=5]
Top down: pointer chasing Start with //A, navigate down to //A/B and then to //A/B/C, and then check values of C Bottom up: reverse pointer chasing Start with //C[.=5], navigate up to //B[/C[.=5]] and then to //A[/B/C[.=5]] Hybrid: top down and bottom up, meet in middle Start with //A, navigate down to //A/B Start with //C[.=5], navigate up to //B[/C[.=5]] Intersect B nodes )In general, hybrid can combine multiple top-down and bottom-up plans starting from anywhere in the path expression
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Comparison of Lore navigational plans
Which plan is best depends on the size of the intermediate results it generates Choose the optimal join order! Top down and bottom up are essentially index nested-loop joins (“pure” navigation) Hybrid can use any join strategy to combine subplans
Structural approach
Binary containment joins (Al-Khalifa et al., ICDE 2002) Given Alist and Dlist , two lists of elements encoded with ( left , right ), with each list sorted by left Find all pairs of ( a , e ), where a ∈ Alist and e ∈ Dlist , such that a is a parent (or ancestor) of e
Example query processing scenario: //book/author Using an inverted-list index, retrieve the list of book elements sorted by left , and the list of author elements sorted by left Find pairs that actually form parent-child relationships
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Tree-based algorithms
Algorithm Tree-Merge-Anc
BeginJoinable = 0;
For each a in Alist :
Start from BeginJoinable and skip Dlist until the
first element with left > a. left ; update BeginJoinable ;
Start from BeginJoinable and join each d from
Dlist with a ; stop at the first d with left > a. right ;
An alternative algorithm, Tree-Merge-Desc , uses Dlist
as the outer table instead of Alist , and requires
minor tweaks to conditions
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Tree-Merge-Anc example
a 1 : BeginJoinable = d 1 ; stops at d 4
a 2 : BeginJoinable = d 2 ; stops at d 4
a 3 : BeginJoinable = d 4 ; stops at d 6
a 4 : BeginJoinable = d 6
) Further optimization is possible to avoid unnecessary rescanning; though in general rescanning cannot be avoided
a 1 a 2
a 3 a 4
d 1 d 2 d 3
d 4 d 5 d 6
Worst case of Tree-Merge-Anc
Optimal (up to a
constant factor) for //
Not optimal for /
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Worst case of Tree-Merge-Desc
Not even optimal
for //
) Problem: linear
access to Alist forces
unnecessary
scanning
) Idea: create another
representation that
corresponds more
closely to a tree
traversal
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Stack-based algorithms
Algorithm Stack-Tree-Desc Start with an empty stack Astack
While Astack or Alist or Dlist is not empty: If heads of both Alist and Dlist come after the top of Astack , pop Astack ; Else if the head of Alist is contained by the top of Astack , push it onto Astack and advance Alist ; Else join the head of Dlist with everything on Astack and advance Dlist ;
) Output is ordered by Dlist
An alternative algorithm, Stack-Tree-Anc , orders output by Alist but requires more bookkeeping
Compact encoding using stacks
One stack for each node in the query twig
Elements in a stack form a containment chain
Each stack element points to one in the parent stack
Specifically, the top one that contains it
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PathStack
Handles twigs with no branches q 1 // q 2 //…// qn
Input lists T (^) q 1 , T (^) q 2 , …, T (^) qn and stacks Sq 1 , Sq 2 , …, Sqn While T (^) qn is not empty: Let T (^) qmin be the list whose head has smallest left ; Clean all stacks: pop while top’s right < head ( T (^) qmin ). left ; Push head ( T (^) qmin ) on Sqmin , with pointer to top ( Sparent ( q min) ); If q min is the leaf ( qn ), output results and pop Sqmin ;
Check properties Elements in a stack form a containment chain Each stack element points to the top one in the parent stack that contains it
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Extending PathStack to TwigStack
A first cut Decompose a twig into root-to-leaf paths Process each path using PathStack Merge solutions for all paths
Problem: intermediate results may be big
All authors will be returned by PathStack , though only the last one should be in the final result
TwigStack
Generate solutions for each root-to-leaf path
Do not use PathStack , which generates all solutions Modify PathStack to generate only solutions that are parts of the final result (possible if twig contains only //) Specifically, when pushing h (^) q onto stack Sq , ensure that
- h (^) q has a descendent h (^) q’ in the each input list Tq’ where q’ is a child of q
- Each h (^) q’ recursively satisfies the above property
Merge solutions for all paths
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TwigStack still suboptimal for /
Example
Desired result: ( A 1 , B 2 , C 2 ), ( A 2 , B 1 , C 1 )
Initial state: all three stacks empty; ready to push one of A 1 , B 1 , C 1 onto a stack
If we want to ensure that non-contributing nodes are never pushed onto the stack, then Cannot decide on A 1 unless we see B 2 and C 2 Cannot decide on B 1 or C 1 unless we see A (^2)
A 1 A 2 B 1 C 1
B 2 C 2
A B C
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Optimization using an index
Idea: if there are indexes on input lists ordered by left , use these indexes to skip lists more efficiently
Example: Niagara’s ZigZag join on A//B
After advancing to the second A, use the index on B list to go directly to the first joining B, instead of scanning B list linearly When processing a B, use the index on A list to skip
