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from the seminarsupport for non-standard datatypes in dbms

Held by Brendan Briody

Accelerating XPath Location Steps

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Overview1. Introduction

- Awareness of tree structured data (XML ...).

- Problem with recursion and RDBMS.

2. Tree Traversals & Mappings (part 1)- Traversing trees to obtain information. - pre and post mapping to orthogonal coordinates, discovering their relationships and introducing corresponding XPath axes.

3. Axes and Query windows - Representing nodes in 5- dimensional descriptors and defining query

windows for XPath axes.

4. Representation in SQL- Applying descriptors to a relational table and performing analogue SQL queries according to XPath expressions.

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5. Shrink-Wrapping the // Axis Discovering equations to shrink-wrap window ranges to minimise query Query time comparison shrunk and non-shrunk windows.

6. Tree Mapping (part 2) Stretching - a different pre/post node assignment idea to avoid misled query scans of shrink-wrapping. Advantages / Drawbacks of shrinking

and stretching.

7. Benchmarking Accel – Schema against Edge Mapping

Performance tests in query time in dependency of document sizes and tree variations.

Overview

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1. Introduction

Awareness of tree structured data in the everyday ITworld and combination with RDBMS.

How can we achieve this ?

RDBMS

Gain information independent of tree type ! >>

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2. Tree traversals & Mappings (part 1)

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2. Tree traversals & Mappings (part 1)

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3.1 XPath Major Axes

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4. Axes and Range QueriesWe have now successfully transformed recursive queries into range queries.To support all XPath Axes though we need a little more information.

- child / parent , following / preceding siblings „par(v)“ value characterises these axes too - attribute is distinguished by a att(v) Boolean - tag(v ) holds the node or attribute name

The result is a 5-Dim descriptor but giving us a 5-dimensional region:

descr(v) = (pre(v),post(v),par(v),att(v),tag(v))

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Axis αQuery window(α,v)

pre postpost par att tag

child <(pre(v), ) , [[0,post(v)))

, pre(v)

, false

,* >

descendant <(pre(v), ) , [[0,post(v))) , * ,

false,* >

descendant-or-self <[pre(v), ) ,

[[0,post(v)]] , * , false

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parent <[par(v), par(v)]

, ((post(v), )) , * ,

false,* >

ancestor <[0,pre(v)) , ( (post(v), )) , * ,

false,* >

ancestor-or-self <[0,pre(v)] , [[post(v), )) , * ,

false,* >

following <(pre(v), ) , ( (post(v), )) , * ,

false,* >

preceding <(0,pre(v)) , ((0,post(v))) , * ,

false,* >

following-sibling <(pre(v), ) , ( (post(v), )) , par() ,

false,* >

preceding-sibling <(0,pre(v)) ,

((0,post(v))) , par() , false

,* >

attribute <(pre(v), ) , [[0,post(v)))

, pre(v) , true ,*

>

Now instead of discrete pre/post values we define intervals [..) , (..].. (..) ....

4. Axes and Query windows

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Specify SQL relational scheme with descriptor.

5-column Table accel

Pre value can be considered as primary key

Query(e /α) = SELECT v’.* FROM Query(e) v , accel v’

WHERE v’ INSIDE window(α,v)

Idea of rectangular region query windows in pre /post plane. Optimised support by R- and B-Trees. To be continued..

4. Representation in SQL

pre post par att tag

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4. Representation in SQLCreating conventional SQL Queries from XPath expressions:Ex.: /descendant::n1/preceding-sibling::n2We get

SELECT v2.* FROM accel v1, accel v2 WHERE 0 < v1.pre AND v1.tag = n1 AND v2.pre < v1.pre AND v2.post < v1.post AND v2.par = v1.par AND v2.tag = n2

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5. Shrink wrapping the // axisKnowledge taken from specific properties of pre/post ranks to shrink window

size(e) = level(e)- pre(e) + post(e) (1) 3 = 2 - 3 + 4

For the right most leaf of the sub treewe can say

size(e) = pre(h) - pre(e) (2) 3 = 6 - 3

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Using height(t) instead of level(e):

Node h has max pre-order and node f has min post order rank

pre(h) ≤ post(e) + height(t)

post(f) ≥ pre(e) – height(t)

The value height(t) of a document tree is assigned at document loading time.

From equation(2)formed to pre(h) = pre(e) + size(e) and replacing size(e) with (1) leads to pre (h) = post(e) + level(e)

For a useful estimation we can also for sure say that:Level(e) ≤ height(t)

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5. Shrink wrapping the // axis

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5. Shrink wrapping the // axis

Attribute and leaf „l“ access

Knowledge of pre(l) and post(l) differingby height:post = pre – height(t)

We are left with a shrunk-wrapped regionthat minimizes query time considerably.

With a B-tree based XPath accelerator on top of a IBM DB2 and an XML instance of 1.1 MB (21051 nodes) we get

Query t shrunk [s] t[s] # Nodes

//open_auction//description 0.2 53 120

//open_auction//description//listitem 0.32 55.5 126

//open_auction//description//listitem//keyword 0.34 124 90

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Independent pre/post scans result to possible results but also yield false hits.

6. Tree Mapping (part 2)

False pre scan hits

False post scan hits

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6. Tree Mapping (part 2)Use a different type of pre post assignment to avoid false pre post scans

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Called stretching

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6. Tree Mapping (part 2)

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6. Tree Mapping (part 2)

Advantages and drawbacks of stretching:

- avoids incorrect pre post scans by stretched mappings a seen in previous slide- all axis query windows work as before- pre and post of a context node are still unique- estimation of subtree size is accurate : size(v) = ½ (post(v) - pre(v) –1)- relationships are still maintained due to relationships and not absolute values.

Drawback: The pre and post values are not dense.

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7. Benchmarking Accel – Schema against Edge Mapping

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time[

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Measurements performed on:Intel i586 ~ 1 GHz CPU,2.4 Linux Kernel, ext2 Filesystem, EIDE hard disk, 256 MB RAMNo other processes active

File size [MB] 0,11 0,55 1,1 11 55 110

Edge map [s] 0,17 0,7 1,5 20,4 98,8 197

XPath Accel[s] 0,03 0,25 0,34 2,4 22,9 44