DOGMA: A Disk-Oriented Graph Matching algorithm

Presented By: Jasmeet Jagdev

• Increasing size of RDF databases

• No graph-based disk-resident index developed so far

Motivation

Snapshot of GovTrack database

Query

• DOGMA Index

• Query Processing Algorithm

Outline

• Indexing Algorithm

• DOGMA_basic

• DOGMA_adv

• Extensions of index

• DOGMA_ipd

• DOGMA_epd

• Experimental Results

• Notations

S – Subjects P – Properties V - Values

is a triple Sets

A graph A Query graph

Answer =

Notations

k-merge

Let G1, G2 be two RDF graphs

G1 G2

V1

V2

Vm

DOGMA Index

• It is a balanced binary tree DR

• It has order k ( k>=2)

• Each node = size of disk page

• Each node is labeled by a graph

• Label of leaf node correspond to partition of GR

• Label of parent Node = k-merge of graphs labeling

the children

DOGMA Index

Indexing Algorithm

u

v

m

u

v

m

u m+v

u m+v

e

e+x+g x

g

e g

e+g

Indexing Algorithm (contd..)

• Keeps moving from level Gj… G0

• Recursively builds the

tree

• Uses an external graph partitioning algorithm

Indexing Algorithm (contd..)

Complexity

• Worst-case time complexity is :

= Number of Vertices

= Worst-case complexity of Graph Partitioning Algorithm

Query Processing Algorithm

• Assumes existence of two index retrieval functions

1.

2.

• Types

1. DOGMA_basic

2. DOGMA_adv

DOGMA_basic

DOGMA_basic (contd..)

Complexity

• Worst-case time complexity is :

= Number of Vertices

= Number of Variables

• Introduction of distance constraint

• Distance index is also maintained

• All –pair shortest path – not calculated • Worst case time complexity O(|V|3) • Space complexity O(|V|2)

• Construct two lower-bound distance indexes • DOGMA_ipd • DOGMA_epd

• Approximation techniques are used to achieve acceptable complexities

DOGMA_adv

Distance condition

Distance condition

DOGMA_adv (contd..)

DOGMA_ipd

• Ipd - Internal Partition Distance

• Distance from the Vertex to the outside of the subgraph

P

N M

v u

• This distance is stored as closest approximation

Complexity of Building DOGMA_ipd

• Worst-case time complexity is :

• Worst-case space complexity is :

Using DOGMA_ipd

DOGMA_epd

• epd - External Partition Distance

• Distance from the Vertex to other subgraph (denoted by a color)

P

N M

v u

• epd(v,blue) = distance from v to blue-colored subgraph

Using DOGMA_epd

Complexity of Building DOGMA_epd

• Worst-case time complexity is :

• Worst-case space complexity is :

Experimentation

• Database systems used for comparison

• Sesame2

• Jena2

• JenaTDB

• SwiftOWLIM

• RDF datasets used

• GovTrack – 14.5 m (well connected)

• LUBM – 13.5 m (sparse and loosely connected)

• Flicker social network – 16 m (well connected and

dense)

Experimental Results Low complexity

Experimental Results Low complexity

Experimental Results High complexity

Experimental Results High complexity

Experimental Results Storage requirement