XPathLearner: An OnLine SelfTuning Markov Histogram for XML Path Selectivity Estimation

1
XPathLearner An On-Line Self-Tuning Markov
Histogram for XML Path Selectivity Estimation

• Authors Lipyeow Lim, Min Wang, Sriram
  Padmanabhan, Jeffrey Scott Vitter, Ronald Parr
• Speaker Ho Wai Shing

2
Contents

• Introduction the problems in XML path
  selectivity estimation
• XPathLearner the properties and the details
• Experiment Results
• Conclusions
• Future Work

3
Introduction

• XML is becoming the standard of data exchange
• We need to query the structure and text data of
  XML documents
• Selectivity is essential in optimizing evaluation
  plans

4
Introduction

• Example

5
Introduction

• Example

FOR b IN document("")//bookWHERE b/publisher
"Morgan Kaufmann" AND b/year "1998"RETURN
b/title The path expressions //book/publisher
"Morgan Kaufmann"//book/year
"1998"//book/title
6
Introduction

• We need a structure to store some statistics of
  the data
• Then calculate the estimated selectivity from
  these statistics
• Problem estimate the selectivity of (simple,
  single-value, multi-value) path expressions with
  limited space

7
Related Work

• Path Trees
• Markov Tables
• k-RO (in Lore)

8
Path Trees

• Aggregate siblings with the same tag
• tag names only (no data values)
• e.g.,

9
Markov Table

• selectivity of short paths up to length k is
  stored
• selectivity of longer paths are estimated using a
  Markov model
• e.g.,

10
k-RO

• used in Lore systems
• very similar to Markov table
• data values are also objects
• stored as a graph

11
Twigs

• can answer "twig" queries
• a structural query with a small branch
• based on suffix tree (for simple paths)
  signatures in each node (for estimating
  branching)

12
Problems Faced

• Offline
• need to scan the whole repository beforehand to
  gather statistics
• unfeasible if the data is remote and is extremely
  large
• Can solve SPEs only or it's too large
• Ignore data values

13
Problems Faced

• Not Adaptive to query workload
• much space wasted in infrequently asked paths
• No Quick Update
• needs periodic rescan of repository

14
Objective

• XPathLearner
• uses Markov based approach,
• uses an online algorithm,
• is adaptive to workload,
• can answer simple paths, single-value paths
  (//A/B'3') and multi-value paths
  (//A'2'/B'3').
• considers data values,
• can be easily updated

15
XPathLearner
16
Architecture
17
A More Detailed Example
18
What to Store?

• Markov table (1st order in the discussion)

19
What to Store?

• may be large if there are many data values
• solution only "tag-tag", "tag", and top-k value
  entries are stored exactly, other entries are
  stored within buckets
• default is 1

20
What is Actually Stored?

• Compressed 1st order Markov table (or, Markov
  histogram)

assumption v1-v4 starts with 'a', v5-v8 starts
with 'b', k 1
21
How to Retrieve Selectivity?

• Use this formula
• ? selectivity
• t1, t2, ..., tn tags
• t1t2...tn path with these tags
• N total number of data items

22
How to Retrieve Selectivity?

• Use this formula (it's what we calculate)
• ? selectivity
• t1, t2, ..., tn tags
• t1t2...tn path with these tags
• f(p) frequency of the path p

23
How to Retrieve Selectivity?

• Use this formula (if it's multi-valued)
• ? selectivity
• t1, t2, ..., tn tags
• t1t2...tn path with these tags
• f(t,v) frequency of the value v in tag t

24
Retrieval Example

• for path //B/C/D, estimated selectivity
• for path //B/C/Dv3, estimated selectivity

25
How to Update?

• get the query feedback, e.g., (BCD, 5)
• update the histogram entries that contained in
  the query so that the future estimation could be
  more accurate
• e.g., update B, C, D, BC, BD so that the
  estimation is nearer to 5 than before.
• two update approaches the Heavy-tail Rule, the
  Delta Rule

26
Heavy Tail Rule

• put more correction towards the end (tail) of the
  path
• equation
• fk() refers to the frequency before update
• fk1() refers to the frequency after update
• suggestion wi 2i

27
Heavy Tail Rule

• updating those one-'tag' entries
• safeguards the terms that were set by exact query
  feedback

28
Heavy Tail Rule

• A reminder to what is stored

29
Heavy Tail Rule

• Example query feedback (ACD, 6)
• by the table, estimation f(AC) / f(C) x f(CD)
  3 / 7 x 6 ? 3

30
Heavy Tail Rule

• updates
• new estimation 4 / 8 x 8 4

31
Delta Rule

• first proposed by Rumelhart et al.
• basic idea
• where

32
Experiments
33
Experiments

• Data Set DBLP (other experiments are done but
  not included in the paper)
• Metric average absolute error, average relative
  error

34
Experiments
35
Experiments
36
Experiments
37
Experiments
38
Experiments
39
Conclusions

• XPathLearner is a new method for estimating the
  selectivity of path expressions
• It is online, based on query feedback and doesn't
  need database scan
• use Markov histograms to store statistics

40
Future Work

• change from fixed length Markov table to variable
  length Markov table
• choose the paths to be stored more carefully or
  wisely
• apply the update method to other areas, e.g.,
  graph based structures, to answer branching
  queries, etc

41
References

• 1Lipyeow Lim, Min Wang, Sriram Padmanabhan,
  Jeffrey Scott Vitter, Ronald Parr, XPathLearner
  An On-Line Self-Tuning Markov Histogram for XML
  Path Selectivity Estimation, VLDB'02