structural joins on xml documents
DESCRIPTION
TRANSCRIPT
Efficient Querying of XML Data Using Structural Joins
Efficient Querying of XML Data Using Structural Joins
ContentContent
A quick look at XML query languages
Lore - an example of a native XML database
DB2 - an example of RDBMS’s support for XML
On supporting containment queries in RDBMS
The Tree-Merge and Stack-Tree algorithms
The StackPath algorithm
XMLXML
Replacement for HTML– Focus is on storing and processing.
Electronic Data Interchange– Querying becomes desirable.
People with many XML documents actually have an XML database.
XML query languagesXML query languages
XML-QL– Influenced by SQL– Submitted to W3C (lost favor to XQuery)
XPath– used in XSLT– the basis for path expressions in XQuery
XQuery– A W3C working draft (version 1.0)– Based on Quilt (which in turn was mainly influenced
by XML-QL and Lorel)– No updates, limited IR features
XPathXPath
1. */para1. selects all para grandchildren of the context node
2. /doc/chapter[5]/section[2]1. selects the second section of the fifth chapter of the doc
3. chapter//para1. selects the para element descendants of the chapter element
children of the context node
4. para[@type="warning"]1. selects all para children of the context node that have a type
attribute with value warning
5. chapter[title="Introduction"]1. selects the chapter children of the context node that have one or
more title children with string-value equal to Introduction
XQueryXQuery
document("books.xml")//chapter/title– Finds all titles of chapters in document books.xml
document(bib.xml")//book[publisher = "Addison-Wesley”AND @year > "1991"]– Finds all books in document bib.xml published by Addison-
Wesley after 1991 <results> {
FOR $t IN distinct(document("prices.xml")/prices/book/title)
LET $p := avg(document("prices.xml")/prices/book[title=$t]/price)
WHERE (document("bib/xml")/book[title=$t]/publisher) = "Addison-Wesley"
RETURN
<result> { $t } <avg> { $p } </avg> </result>
} </results>
– Returns the title and average price of all books published by Addison-Wesley
XML documents as treesXML documents as trees
<book year=“2000”>
<title> XML </title>
<authors>
<author> Bill </author>
<author> Jake </author>
</authors>
<chapter>
<head> History </head>
<section>
<head> … </head>
<section> … </section>
</section>
<section> … </section>
</chapter>
<chapter> … </chapter>
</book> Order of nodes is important
book
year title authors chapter chapter
2000 XML author head section section
Bill Jake
author
History head section
...
...
......
XML documents as treesXML documents as trees
<book year=“2000”>
<title> XML </title id=“id1”>
<authors>
<author> Bill </author>
<author> Jake </author>
</authors>
<chapter>
<head> History </head>
<section>
<head> … </head>
<section> … </section idref=“id1”>
</section>
<section> … </section>
</chapter>
<chapter> … </chapter>
</book> Order of nodes is important
book
year authors chapter chapter
2000 xml author head section section
Bill Jake
author
History head
...
...
......
title
section
Executing queriesExecuting queries
How does one execute a complex query:– Parse the query (i.e. break it down to basic operations).– Let a query optimizer devise a corresponding physical query
plan.– Execute the required basic operations combining the
intermediate results as you go.
The most common basic operations are:– Finding nodes satisfying a given predicate on their value.– Finding nodes satisfying a given structural relationship.
XML databasesXML databases
XML is semi-structured; data items may have missing elements or multiple occurrences of the same element.It may even not have a DTD.
Native semi-structured databases– X-Hive, Lore
RDBMS– Oracle– SQL-Server– DB2
All added support for XML
Semi-structured XML databasesSemi-structured XML databases
There aren’t many around
Store XML files plus indexes
Usually build (and store) most or all of the tree
Usually solve path expressions by pointer-chasing
LOREAn example of a native semi-structured
database
LOREAn example of a native semi-structured
database
Lore - sample databaseLore - sample database
Select x
From DBGroup.Member x
Where exists y in x.age: y<30
Lore - data modelLore - data model
Called the Object Exchange Model The data model is a graph (though the reference edges
are marked as such). Each vertex is an object with a unique object identifier. Atomic objects have no outgoing edges and contain
values (like strings, gifs, audio etc.) All other objects may have outgoing edges. Tag-Names (labels) are attached to the edges, not the
vertices. Objects may optionally have aliases (names).
As is obvious this is just another view of our XML tree
Lore - indexesLore - indexes
Vindex (value index) - implemented as a B+-tree– Supports finding all atomic objects with a given incoming edge
label satisfying a given predicate. Lindex (label index) - implemented using extendible hashing
– Supports finding all parents of a given object via an edge with a given label.
Bindex (edge index)– Supports finding all parent-child pairs connected via a given
label. This is useful for locating edges with rare labels.
In addition there are some other indexes (not important to us).
Note that we need more indexes than in a relational database
Lore - statistics (partial list)Lore - statistics (partial list)
For each labeled path p of length <= k (usually k=1):
– The total number of instances of p, denoted |p|
– The total number of distinct objects reachable via p,denoted |p|d
– The total number of l-labeled edges going out of p,denoted |p l|
– The total number of l-labeled edges coming into p,denoted |p l|
Lore - path expressions (simplified)Lore - path expressions (simplified)
Simple path expressions– x.l y
Path expressions– an ordered list of simple path expressions
– x.l y, y.l2 z
Path expressions logical plan:
x.B y, y.C z, z.D v
Lore - basic physical operators (slightly edited)Lore - basic physical operators (slightly edited)
Scan(father, label, son)– Finds all the sons of a given father (through a given label).Does pointer-chasing
Lindex(father, label, son)– Finds all the fathers of a given son (through a given label).Uses the Lindex
Bindex(label, father, son)– Finds all the father-son pairs connected by a given label.Uses the Bindex
Vindex(label, operator, value, atomic-object)– Finds all the the atomic objects with a given label incoming label
satisfying the given predicate.Uses the Vindex
Name(alias, node)– Verifies that the specified node has the given alias.
Lore - physical path subplansLore - physical path subplans
x and y are unbound y is bound x and y are unbound
The estimated hit-rate (per x) of scan(x, “C”, y) is: (|B C| / |B|d)
The estimated hit-rate (per y) of Lindex(x, “C”, y) is: (|C B| / |C|d)
Lore - sample logical planLore - sample logical plan
Select x From DBGroup.Member x Where exists y in x.age: y<30
– Glue nodes are pivot points, they recursively evaluate the cost of evaluating their sons in left-right or right-left order.
Lore - sample physical subplansLore - sample physical subplans
(a) corresponds to a possible left-right plan of the top “glue” (b) corresponds to a possible left-right plan of the right “glue” (c) corresponds to a possible right-left plan of the right “glue” (d) corresponds to a possible right-left plan of the top “glue”, using (c)
Lore - path expressions strategiesLore - path expressions strategies
A higher level view of path expressions solving
Top-Down– Look for all Member objects in DBGroup and for each one look for
Age subobjects with a value < 30.uses scan
Bottom-up– Look for all atomic objects with value < 30 and for each one walk up
the tree using only Age-labeled followed by Member-labeled edges.uses Vindex and then Lindex
Hybrid– Do Top-Down part of the way and Bottom-Up part of the way.
Select x From DBGroup.Member x Where exists y in x.age: y<30
Lore - path strategies (continued)Lore - path strategies (continued)
Top-Down is better when there are few paths satisfying the required structure, but many objects satisfying the predicate.
Bottom-Up is better when there are a few objects satisfying the predicate but many paths satisfying the required structure.
Hybrid is better when the fan-out degree (going down), increases at the same time the fan-in degree (going up) does.
DB2An example of a RDBMS support of
XML
DB2An example of a RDBMS support of
XML
DB2 - XML support DB2 - XML support
XML column– An entire XML document is stored as a column in a table.– may be XMLCLOB, XMLVARCHAR or XMLFile.– You define which XML elements or attributes should be
extracted to indexed columns in side tables.
– UDF’s are provided for inserting, updating and selecting fragments of a document.
XML collection– Compose an XML document from existing DB2 tables.– Decompose an XML document and retrieve some of it into a set
of DB2 tables.– Basically a conversion mechanism.
– Stored procedures automate most of the work.
DB2 - a nice diagram...DB2 - a nice diagram...
DB2 - example Data Access DefinitionDB2 - example Data Access Definition
DB2 - example DAD (continued)DB2 - example DAD (continued)
DB2 - searching XML documentsDB2 - searching XML documents
Well, whatever is in the side tables is queried using SQL.
What about things not in any side table?
– A loosely coupled IR engine (part of the DB2 Text Extender) is called using a UDF to take care of this.
– The UDF’s use a syntax compatible with XPath.
DB2 - conclusions (in a nutshell)DB2 - conclusions (in a nutshell)
Pros– Integrated solution which automates a lot of work.– We can ask queries that mix data from XML and the regular
database tables (aka “web-supported database queries” and “database-supported web queries”).
Cons– One has to manually define the mappings between the XML
documents and the tables.– Is it fast enough?
On Supporting Containment Queries in RDBMS
On Supporting Containment Queries in RDBMS
Zhang, Naughton, DeWitt, Luo, Lohman
ACM SIGMOD 2001
Article goalsArticle goals
Given that a lot of XML data is (and will probably be) stored in RDBMS which is the best way to support containment queries?
– Using a loosely coupled IR engine?
OR
– Using the native tables and query mechanisms of the RDBMS?
Structural relationships in treesStructural relationships in trees
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15book
year title authors chapter
2000 XML author head section
Bill Jake
author
History head
pre-order book
year title authors chapter
2000 XML author head section
Bill Jake
author
History head
post-order
Note that x is a descendant of y if and only if:preorder(x) > preorder(y) and postorder(x) < postorder(y)
y is the father of x if in addition: level(x) = level(y) + 1
Structural relationships in XMLStructural relationships in XML
The previous observations are true even if we look at any monotone functions of the preorder and the postorder numbers.
The start and end position of an element in an XML document are exactly such monotone functions.
In other words we can use a small extension of the regular
IR inverted-index to also solve structural relationships!
Note that we have a problem of adapting the numbers if the document changes.
The inverted indexesThe inverted indexes
An Elements index (E-Index): Holds for each XML element, the docno, begin, end and level of every occurrence of that element.
A Text index (T-Index): Holds for each text word, the docno, wordno and level of every occurrence of the word.
Experiment planExperiment plan
Compare the following two systems:
An inverted list engine supporting containment queries on XML data.– The engine was built (due to lack of a commercial one).– The code was written in C++ and the inverted-indexes were
stored in a B+-tree with each list stored as a record.– Each list is in ascending order of docno, begin (or wordno).– An in-house algorithm was developed for evaluating simple
containment queries. A full RDBMS approach (tried DB2 7.1 and SQL-Server 7.0)
– The E-index and T-index are stored as the following tables: ELEMENTS(term, docno, begin, end, level)TEXTS(term, docno, wordno, level)
Note that we do not use the IR engine of the RDBMS.
Using the inverted indexes tablesUsing the inverted indexes tables
E//"T”
select * from ELEMENTS e, TEXTS t
where e.term = ’E’ and t.term = ’T’
and e.docno = t.docno
and e.begin < t.wordno and t.wordno < e.end
E="T"
select * from ELEMENTS e, TEXTS t
where e.term = ’E’ and t.term = ’T’
and e.docno = t.docno
and e.begin + 1 = t.wordno and t.wordno + 1 = e.end
In a similar fashion we solve Elements only queries, father-son, and words distance queries.
(how will this look for E//E ?)xy
xy x
y
Experiment setupExperiment setup
The data sets:
Experiment setup (continued)Experiment setup (continued)
The queries are all simple queries of the form: E//T, E//E, E/T or E/E
Experiment resultsExperiment results
Results analysisResults analysis
Why did DB2 perform better in QS4, QD4 and QG5?
Remember that each list in the inverted engine is stored as one record!
Why did DB2 perform worse in all the other queries?– Bad optimizer decisions?– Is I/O more expensive (locking, security, etc.)?– Other factors?– It turns out that the queries are CPU-bound!
Further investigation found out that it was the merge algorithm.
DB2 merge algorithmsDB2 merge algorithms
When joining on:
a.docno = d.docno and a.begin < d.wordno and d.wordno < a.end
Standard Merge-Join only uses the a.docno = d.docno predicate (since it does one comparison, using one index per table), and applies the rest of the condition on each matching couple.
Hash-Join only uses the a.docno = d.docno predicate (since it can not handle inequalities anyway), and thus performs similarly to the classical merge join.
Index nested-loop join looks, for each row in the outer table, for all rows in the inner table index that lie between a start-key and astop-key.
Assuming the outer table is ELEMENTS and the inner table is TEXTS:
– start-key: term = value and docno = outer.docno and wordno > outer.begin
– end-key: term = value and docno = outer.docno and wordno < outer.end
The Multi-Predicate Merge JoinThe Multi-Predicate Merge Join
begin-desc = Dlist->first node; OutputList = NULL;
for (a = Alist->firstNode; ; a = a->nextNode) {
d = begin_desc;
while (d.docno < a.docno) d = d->nextNode;
if (a.docno < b.docno) continue;
while (d.begin <= a.begin) d = d->nextNode;
begin_desc = d;while (d.begin < a.end) { // implies d.end < a.end
if (a.docno < b.docno) break;
append (a,d) to OutputList;
d = d->nextNode;
}
}
doc begin end
5 7 20
5 14 19
5 21 28
5 22 27
5 29 31
5 32 40
doc begin
5 2
5 23
5 24
5 33
5 37
5 42
Alist Dlist
Comparison of the merge algorithmsComparison of the merge algorithms
It seems like the NLJ algorithm will usually compare less items, BUT It has to spend time on index seeks! It uses random access so cache utilization is poor.
MPMGJN & traditional joins - statisticsMPMGJN & traditional joins - statistics
Note: DB2 did not choose NLJ for QG4
Structural Joins: A Primitive for Efficient XML Query
Pattern Matching
Structural Joins: A Primitive for Efficient XML Query
Pattern Matching
Al-Khalifa, Jagadish, Koudas, Patel, Srivastava, Wu
ICDE 2002
Structural-Join algorithmsStructural-Join algorithms
Tree-Merge-Anc (aka MPMGJN) Tree-Merge-Desc Stack-Tree-Desc Stack-Tree-Anc
The ?-?-Anc algorithms produce the output sorted by the ancestors.
The ?-?-Desc algorithms produce the output sorted by the descendants.
The sorting variant to use depends on the way an optimizer chooses to compose a complex query.
Based on the (docId, startPos, endPos, level) information of XML elements and attributes.
Given two lists of potential ancestors and potential descendants, both in ascending order of docId+startPos, the following structural join algorithms are presented:
Tree-Merge-AncTree-Merge-Anc
begin-desc = Dlist->first node; OutputList = NULL;
for (a = Alist->firstNode; ; a = a->nextNode) {
d = begin_desc;
while (d.startPos <= a.startPos) d = d->nextNode;
begin_desc = d;
while (d.startPos < a.endPos) { // implies d.endPos < a.endPos
if (a.level +1 != d.level) continue; // father-son
append (a,d) to OutputList;
d = d->nextNode;
}
}
Note: For ease of exposition, we assume that Alist and Dlist have the same docId.
Analysis of Tree-Merge-AncAnalysis of Tree-Merge-Anc
Ancestor-Descendant structural relationships:– O(|Alist| + |Dlist| + |OutputList|)– Since first while loop increases d, and second while loop increases output or a.
Father-Son structural relationships: – O(|Alist| * |Dlist|)
...
...
a1
a2
a3
an
d3d1 d2 dn
begin end
a1 1 4n
a2 2 4n-1
a3 3 4n-2
.
.
an n 3n+1
begin
d1 n+1
d2 n+3
d3 n+5
.
.
dn 3n-1
Alist Dlist
Can sub-sorting on levelNum help ?
Tree-Merge-DescTree-Merge-Desc
begin-anc = Alist->first node; OutputList = NULL;
for (d = Dlist->firstNode; ; d = d->nextNode) {
a = begin_anc;
while (a.endPos <= d.startPos) a = a->nextNode;
begin_anc = a;
while (a.startPos < d.startPos) {
if (a.level +1 != d.level) continue; // father-son
if (d.endPos < a.endPos) append (a,d) to OutputList;
a = a->nextNode;
}
}
Note: For ease of exposition, we assume that Alist and Dlist have the same docId.
Analysis of Tree-Merge-DescAnalysis of Tree-Merge-Desc
Ancestor-Descendant and Father-Son structural relationships: – O(|Alist| * |Dlist|).– Works in linear time on most real data.
...
begin end
a0 1 4n+2
a1 2 5
a2 6 9
a3 10 13
.
.
an 4n-2 4n+1
begin
d1 3
d2 7
d3 11
.
.
dn 4n-1
Dlist Alist
a0
a3a1 a2 an
d1 d2 d3 dn...
Stack-Tree algorithmsStack-Tree algorithms
Motivation
– A depth-first traversal of a tree can be performed in linear time, using a stack as large as the height of the tree.
– An ancestor-descendant structural relationship is manifested as the ancestor appearing higher on the stack than the descendant.
– Unfortunately, a depth-first traversal requires going over all the tree.
Stack-Tree-DescStack-Tree-Desc
a = Alist->first node; d = Dlist->first node; OutputList = NULL;
while (lists are not empty) {
e = (a.startPos < d.startPos) ? a : d;
while (e.startPos > stack->top.endPos) stack->pop();if (e == a) { // remember that e.startPos > stack->top.startPos
stack->push(a);
a = a->nextNode;} else // e == d
for each a’ in stack { // Father-Son: If (stack->top.level + 1 = d.level) append(stack->top, d)
append (a’, d) to OutputList;
}
d = d->nextNode;
}
}
Note: For ease of exposition, we assume that Alist and Dlist have the same docId.
Stack-Tree-Desc (father-son example)Stack-Tree-Desc (father-son example)
a1
d1
a2
d2
. .
. .
an
dn
dn+1
dn+2
.
.
d2n
d1 d2n
d2 d2n-1
d3 d2n-2
dn dn+1
a1
a2
a3
an
a1
(a1,d1)
a2
(a2,d2) ...
.
.
.
(an-1,dn-1)
an
(an,dn)(an,dn+1) (an-1,dn+2)
... (a3,d2n-2)(a2,d2n-1)(a1,d2n)
? e.startPos > stack->top.endPos
...
Analysis of Stack-Tree-DecAnalysis of Stack-Tree-Dec
O(|Alist| + |Dlist| + |OutputList|) for ancestor-descendant as well as father-son structural relationships.
– Each Alist element is pushed once and popped once, so stack operations take O(|Alist|).
– The inner “for loop” outputs a new pair each time, so its total time is O(|OutputList|).
– When doing father-son structural joins, we do not even have a “for loop”.
The algorithm is non-blocking.
IO complexity is O(|Alist|/P + |Dlist|/P + |OutputList|/P) where P is the page size.
– Each input page is read just once (and output sent as soon as it is computed).– The stack is as large as the tree height, so it is very reasonable to assume that it
fits in RAM.
Stack-Tree-AncStack-Tree-Anca = Alist->first node; d = Dlist->first node; OutputList = NULL;
while (lists are not empty) {
e = (a.startPos < d.startPos) ? a : d;
while (e.startPos > stack->top.endPos) {
temp = stack->pop();
if (stack->isEmpty()) {
append temp->selfList to OutputList; append temp->inheritList to OutputList;
} else {
append temp->inheritList to temp->selfList; append temp->selfList to stack->top->inheritList;
}
}
if (e == a) { // remember that e.startPos > stack->top.startPos
stack->push(a); a = a->nextNode;
} else { // e == d
for each a’ in stack {
if(a’ == stack->bottom) append (a’, d) to OutputList;
else append (a’, d) to selfList associated with a’
}
d = d->nextNode;
}
} if (!stack->isEmpty()) flush the stack held lists to the outputNote: For ease of exposition, we assume that Alist and Dlist have the same docId.
Stack-Tree-Anc (father-son example)Stack-Tree-Anc (father-son example)
a1
d1
a2
d2
. .
. .
an
dn
dn+1
dn+2
.
.
d2na1(a1,d1)
a2(a2,d2)
.
.
.
(an-1,dn-1)
an(an,dn) (an,dn+1)
(a3,d3),(a3,d2n-2)...(an,dn),(an,dn+1) (a2,d2n-1)
(a1,d2n)
d1 d2n
d2 d2n-1
d3 d2n-2
dn dn+1
a1
a2
a3
an
...
(an,dn), (an,dn+1)
(a2,d2),(a2,d2n-1)...(an,dn),(an,dn+1)
.
.
.
? e.startPos > stack->top.endPos
Analysis of Stack-Tree-AncAnalysis of Stack-Tree-Anc
O(|Alist| + |Dlist| + |OutputList|) For ancestor-descendant as well as father-son structural relationships.
– Assuming the lists are maintained as linked lists with head and tail pointers.
The algorithm is blocking (but only partially).
IO complexity is O(|Alist|/P + |Dlist|/P + |OutputList|/P) where P is the page size.
– We cannot assume that all the lists fit in RAM.– All that we do with lists (except output) is appending.– We can page out a list and we need only keep its tail in RAM. So we need two
extra pages in memory per stack entry - still a reasonable assumption.– We only need to know the address of the head of a list.– Each list page is thus paged out at most once, and paged back in only for output.
Experiment workloadExperiment workload
Experimented with real XML data as well as synthetic data generated by IBM XML data generator (with similar results).
Presented the results for the largest data set: 6.3 million elements (800Mb of data).
Experiment resultsExperiment results
Implemented the structural join algorithms, as well as bottom-up and top-down, on the TIMBER native XML query engine (built on top of SHORE).
Bottom-up and top-down performed poorly:– Even on 10% of the data it took bottom-up 283.5 seconds to run
QS1, and 717.8 seconds for top-down to do it.– It took less than 15 seconds for any of the join algorithms to
complete QS1 on the full data set!
Experiment results (continued)Experiment results (continued)
Implemented the STJ-D as an application program interfacing to a commercial RDBMS through a set of cursors.
Also ran the queries using the RDBMS join mechanisms.
QS1:
Combined: an index on startPos, endPos
Small: up to 10% selectivity, Medium: up to 25%
Experiment results (continued)Experiment results (continued)
Holistic Twig Joins:Optimal XML Pattern Matching
Holistic Twig Joins:Optimal XML Pattern Matching
Bruno, Koudas, Srivastava
ACM SIGMOD 2002
Twig patternsTwig patterns book[title = “XML” AND year = 2000] book[title = “XML”]//author[Fn = “jane” AND Ln = “doe”]
book
year title authors chapter chapter
2000 XML author head section section
Ln title section
...
...
...
Fn
jane doe
author
LnFn
john moe
author
LnFn
john doe
...
XML
...
title
XML
year
2000
book
title
XML
author
Ln
book
jane doe
Fn
Twig patterns
Twig pattern matchingTwig pattern matching
Given a twig pattern Q and an XML database D, a match is a mapping from nodes in Q to nodes in D, satisfying:
– Query node predicates are satisfied by their images.
– The structural relationships between the query nodes are satisfied by their images.
If Q has k nodes, the result may be represented by a relation with k columns.
Twig pattern matching approachesTwig pattern matching approaches
Decompose the twig into a series of binary structural joins, compute each (using STJ-D for example) and join the results.– Note that one may have intermediate results that are very big.
Consider for example: book[title = “XML”]
Decompose the twig into a series of rooted path-expressions, compute each one independently and merge-join the results.– Note that one may have intermediate results that are very big
(but only in different branches).Consider for example: book//author[Fn = “jane” AND Ln = “doe”]
Decompose the twig into a series of rooted path-expressions, compute them simultaneously taking interdependencies into account, and merge-join the results.
PathStack-DescPathStack-Desc
go to start of all lists; OutputList = NULL;
while (lists are not empty) {e = element with minimum startPos in all lists;
i = the list e was taken from; advance list i;
for(int j=1; j < numLists; j++) {
while (e.startPos > stackj->top.endPos) stackj->pop();
}if (e is not from the leaf list) { // remember that for every stack e.startPos > stack->top.startPos
stacki->push(a, &stacki-1->top); // if the I-1 stack is not empty of course
} else { // e is the path query leaf
let (x1, x2, … xnumLists-1) be the linked list whose head is the top of the numLists-1 stack.
For each (y1, y2, … ynumLists-1, e) such that for all j yj is below xj do:
append (y1, y2, … ynumLists-1, e) to OutputList;
}
} Note: For ease of exposition, we assume that all lists have the same docId.
PathStack-Desc (example)PathStack-Desc (example)
a1
b1
a2
b2
c1
b3
c2? e.startPos > stack->top.endPos
a1
b1
a2
b2
c1
b3
c2
b
c
a
a1b1
a2b2
(a2,b2,c1) (a1,b2,c1) (a1,b1,c1) (a1,b3,c2)
b3
PathStack-Desc experimental resultsPathStack-Desc experimental results
Implemented the binary join algorithms, as well as the StackPath, in C++ using the file-system as the storage engine.
Used a synthetic data set made of 1 million nodes with 6 different labels (A1, A2, …A6) uniformly distributed (no information regarding other parameters).
Final remarksFinal remarks
What we did not do (partial list):– Look at using B+-Trees with the stack algorithms.– Look at the TwigStack algorithm.– Look at Kleen-closure evaluation.
Conclusions:
– There is a lot more work to be done by everybody.
Appendix: TwigStack (in a nutshell)Appendix: TwigStack (in a nutshell)
getNext(q) returns a query node such that the head of its list satisfies:– It has the smallest startPos (L) of all the heads of its descendant and sibling lists.– It participates in a solution to the sub-query rooted at that query node.– If it is part of a solution involving its ancestors they were already read.
Appendix (continued)Appendix (continued)
Note that as long as 09 succeeds we return the node whose head has the smallest startPos (L) of all the heads of lists in the sub-tree of q.When 09 fails we “float up” a node whose list head has the the smallest startPos (L) of all the heads of lists in its descendant or sibling lists.
Once a node floats up, its father node’s list does not contain any more ancestors of its list head (otherwise 09 would not fail). Applying the same logic to the father and grandfather etc. leads us by induction to the conclusion that if it this node’s list head is part of a solution involving its ancestors, these ancestors are already out of their lists.
Appendix (continued)Appendix (continued)
Both used ternary trees.– Left sub-tree in (a) has only A1=A2=A3=A4 paths.– Middle sub-tree in (a) has only A1=A5=A6=A7 paths.– Right sub-tree in (a) has solutions. Its size varies (8% to 24% of the tree).– (b): left has no A2 or A3, middle has no A4 or A5, right has no A6 or A7.
BibliographyBibliography Shu-Yao Chien, Zografoula Vagena, Donghui Zhang, Vassilis J. Tsotras, Carlo
Zaniolo, “Efficient Structural Joins on Indexed XML Documents” Proc.of VLDB 2002
Shurug Al-Khalifa, H. V. Jagadish, Nick Koudas, Jingesh M. Patel, Divesh Srivastava, Yuqing Wu, “Structural Joins: A Primitive for Efficient XML Query Pattern Matching”, ICDE 2002
Nicolas Bruno, Nick Koudas, Divesh Srivastava, “Holistic Twig Joins: Optimal XML Pattern Matching”, ACM SIGMOD 2002
Shu-Yao Chien, Vassilis J. Tsotras, Carlo Zaniolo, Donghui Zhang, “Efficient Complex Query Support for Multiversion XML Documents”, Proc. of VLDB 2001
Jason McHugh, Jennifer Widom, “Query Optimization for XML”, Proc. of VLDB 1999
Chun Zhang, Jeffrey Naughton, David DeWitt, Qiong Luo, Guy Lohman, “On Supporting Containment Queries in Relational Database Management Systems”, ACM SIGMOD 2001
Quanzhong Li, Bongki Moon, “Indexing and Querying XML Data for Regular Path Expressions”, Proc. of VLDB 2001
IBM DB2 web site: http://www-3.ibm.com/software/data/db2/
www.w3.org site (on XPath and XQuery)
