This document discusses processing large-scale graphs using Google's Pregel framework. It provides an overview of Pregel, including its map-reduce approach with multiple iterations. An example of using Pregel to calculate connected components in a graph is shown step-by-step. The document also discusses graph algorithms like page rank, bipartite matching, and shortest paths that can be implemented with Pregel and examples of Pregel implementations in systems like Giraph, TinkerPop and ArangoDB.

1. Processing large-scale graphs
,
with GoogleTM Pregel
November 22, 2014
Frank Celler
@fceller
www.arangodb.com

2. About
about us
Frank Celler (@fceller) working on the ArangoDB core
Michael Hackstein (@mchacki) started an experimental
implementation of Pregel
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3. About
about us
Frank Celler (@fceller) working on the ArangoDB core
Michael Hackstein (@mchacki) started an experimental
implementation of Pregel
about the talk
different kinds of graph algorithms
Pregel example
Pregel mind set aka Framework
more examples
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4. Pregel at ArangoDB
Started as a side project in free hack time
Experimental on operational database
Implemented as an alternative to traversals
Make use of the 2exibility of JavaScript:
No strict type system
No pre-compilation, on-the-2y queries
Native JSON documents
Really fast development
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5. Graph Algorithms
Pattern matching
Search through the entire graph
Identify similar components
) Touch all vertices and their neighbourhoods
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6. Graph Algorithms
Pattern matching
Search through the entire graph
Identify similar components
) Touch all vertices and their neighbourhoods
Traversals
De1ne a speci1c start point
Iteratively explore the graph
) History of steps is known
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7. Graph Algorithms
Pattern matching
Search through the entire graph
Identify similar components
) Touch all vertices and their neighbourhoods
Traversals
De1ne a speci1c start point
Iteratively explore the graph
) History of steps is known
Global measurements
Compute one value for the graph, based on all it’s vertices
or edges
Compute one value for each vertex or edge
) Often require a global view on the graph
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8. Pregel
A framework to query distributed, directed graphs.
Known as “Map-Reduce” for graphs
Uses same phases
Has several iterations
Aims at:
Operate all servers at full capacity
Reduce network traZc
Good at calculations touching all vertices
Bad at calculations touching a very small number of vertices
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9. Example – Connected Components
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10. Example – Connected Components
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11. Example – Connected Components
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13. Example – Connected Components
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19. Pregel – Sequence
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20. Pregel – Sequence
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21. Pregel – Sequence
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22. Pregel – Sequence
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23. Pregel – Sequence
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24. Worker ^= Map
“Map” a user-de1ned algorithm over all vertices
Output: set of messages to other vertices
Available parameters:
The current vertex and his outbound edges
All incoming messages
Global values
Allow modi1cations on the vertex:
Attach a result to this vertex and his outgoing edges
Delete the vertex and his outgoing edges
Deactivate the vertex
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25. Combine ^= Reduce
“Reduce” all generated messages
Output: An aggregated message for each vertex.
Executed on sender as well as receiver.
Available parameters:
One new message for a vertex
The stored aggregate for this vertex
Typical combiners are SUM, MIN or MAX
Reduces network traZc
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26. Activity ^= Termination
Execute several rounds of Map/Reduce
Count active vertices and messages
Start next round if one of the following is true:
At least one vertex is active
At least one message is sent
Terminate if neither a vertex is active nor messages were sent
Store all non-deleted vertices and edges as resulting graph
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27. Pregel Questions
connected components
page rank
bipartite matching
semi-clustering
mimum spanning forest
graph coloring
shortest paths
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28. Pagerank
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29. Pagerank
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30. Pagerank
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31. Pagerank
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32. Pagerank for Giraph
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1 public class SimplePageRankComputation extends BasicComputation <
LongWritable , DoubleWritable , FloatWritable , DoubleWritable >
{
2 public static final int MAX_SUPERSTEPS = 30;
34
@Override
5 public void compute ( Vertex < LongWritable , DoubleWritable ,
FloatWritable > vertex , Iterable < DoubleWritable > messages )
throws IOException {
6 if ( getSuperstep () >= 1) {
7 double sum = 0;
8 for ( DoubleWritable message : messages ) {
9 sum += message .get ();
10 }
11 DoubleWritable vertexValue = new DoubleWritable ((0.15 f /
getTotalNumVertices ()) + 0.85 f * sum );
12 vertex . setValue ( vertexValue );
13 }
14 if ( getSuperstep () < MAX_SUPERSTEPS ) {
15 long edges = vertex . getNumEdges ();
16 sendMessageToAllEdges (vertex , new DoubleWritable ( vertex .
getValue ().get () / edges ));
17 } else {
18 vertex . voteToHalt ();
19 }
20 }
21
22 public static class SimplePageRankWorkerContext extends
WorkerContext {
23 @Override
24 public void preApplication () throws InstantiationException ,
IllegalAccessException { }
25 @Override
26 public void postApplication () { }
27 @Override
28 public void preSuperstep () { }
29 @Override
30 public void postSuperstep () { }
31 }
32
33 public static class SimplePageRankMasterCompute extends
DefaultMasterCompute {
34 @Override
35 public void initialize () throws InstantiationException ,
IllegalAccessException {
36 }
37 }
38 public static class SimplePageRankVertexReader extends
GeneratedVertexReader < LongWritable , DoubleWritable ,
FloatWritable > {
39 @Override
40 public boolean nextVertex () {
41 return totalRecords > recordsRead ;
42 }
44 @Override
45 public Vertex < LongWritable , DoubleWritable , FloatWritable >
getCurrentVertex () throws IOException {
46 Vertex < LongWritable , DoubleWritable , FloatWritable > vertex
= getConf (). createVertex ();
47 LongWritable vertexId = new LongWritable (
48 ( inputSplit . getSplitIndex () * totalRecords ) +
recordsRead );
49 DoubleWritable vertexValue = new DoubleWritable ( vertexId .
get () * 10d);
50 long targetVertexId = ( vertexId .get () + 1) % ( inputSplit .
getNumSplits () * totalRecords );
51 float edgeValue = vertexId . get () * 100 f;
52 List <Edge < LongWritable , FloatWritable >> edges = Lists .
newLinkedList ();
53 edges .add ( EdgeFactory . create (new LongWritable (
targetVertexId ), new FloatWritable ( edgeValue )));
54 vertex . initialize ( vertexId , vertexValue , edges );
55 ++ recordsRead ;
56 return vertex ;
57 }
58 }
59
60 public static class SimplePageRankVertexInputFormat extends
GeneratedVertexInputFormat < LongWritable , DoubleWritable ,
FloatWritable > {
61 @Override
62 public VertexReader < LongWritable , DoubleWritable ,
FloatWritable > createVertexReader ( InputSplit split ,
TaskAttemptContext context )
63 throws IOException {
64 return new SimplePageRankVertexReader ();
65 }
66 }
67
68 public static class SimplePageRankVertexOutputFormat extends
TextVertexOutputFormat < LongWritable , DoubleWritable ,
FloatWritable > {
69 @Override
70 public TextVertexWriter createVertexWriter (
TaskAttemptContext context ) throws IOException ,
InterruptedException {
71 return new SimplePageRankVertexWriter ();
72 }
73
74 public class SimplePageRankVertexWriter extends
TextVertexWriter {
75 @Override
76 public void writeVertex ( Vertex < LongWritable ,
DoubleWritable , FloatWritable > vertex ) throws
IOException , InterruptedException {
77 getRecordWriter (). write ( new Text ( vertex . getId ().
toString ()), new Text ( vertex . getValue (). toString ()))
;
78 }
79 }
80 }
81 }

33. Pagerank for TinkerPop3
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1 public class PageRankVertexProgram implements VertexProgram <
Double > {
2 private MessageType . Local messageType = MessageType . Local .of
(() -> GraphTraversal .< Vertex >of (). outE ());
3 public static final String PAGE_RANK = Graph .Key . hide (" gremlin
. pageRank ");
4 public static final String EDGE_COUNT = Graph .Key . hide ("
gremlin . edgeCount ");
5 private static final String VERTEX_COUNT = " gremlin .
pageRankVertexProgram . vertexCount ";
6 private static final String ALPHA = " gremlin .
pageRankVertexProgram . alpha ";
7 private static final String TOTAL_ITERATIONS = " gremlin .
pageRankVertexProgram . totalIterations ";
8 private static final String INCIDENT_TRAVERSAL = " gremlin .
pageRankVertexProgram . incidentTraversal ";
9 private double vertexCountAsDouble = 1;
10 private double alpha = 0.85 d;
11 private int totalIterations = 30;
12 private static final Set <String > COMPUTE_KEYS = new HashSet <>(
Arrays . asList ( PAGE_RANK , EDGE_COUNT ));
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14 private PageRankVertexProgram () {}
15
16 @Override
17 public void loadState ( final Configuration configuration ) {
18 this . vertexCountAsDouble = configuration . getDouble (
VERTEX_COUNT , 1.0 d);
19 this . alpha = configuration . getDouble (ALPHA , 0.85 d);
20 this . totalIterations = configuration . getInt (
TOTAL_ITERATIONS , 30);
21 try {
22 if ( configuration . containsKey ( INCIDENT_TRAVERSAL )) {
23 final SSupplier < Traversal > traversalSupplier =
VertexProgramHelper . deserialize ( configuration ,
INCIDENT_TRAVERSAL );
24 VertexProgramHelper . verifyReversibility (
traversalSupplier .get ());
25 this . messageType = MessageType . Local .of (( SSupplier )
traversalSupplier );
26 }
27 } catch ( final Exception e) {
28 throw new IllegalStateException (e. getMessage () , e);
29 }
30 }
32 @Override
33 public void storeState ( final Configuration configuration ) {
34 configuration . setProperty ( GraphComputer . VERTEX_PROGRAM ,
PageRankVertexProgram . class . getName ());
35 configuration . setProperty ( VERTEX_COUNT , this .
vertexCountAsDouble );
36 configuration . setProperty (ALPHA , this . alpha );
37 configuration . setProperty ( TOTAL_ITERATIONS , this .
totalIterations );
38 try {
39 VertexProgramHelper . serialize ( this . messageType .
getIncidentTraversal () , configuration ,
INCIDENT_TRAVERSAL );
40 } catch ( final Exception e) {
41 throw new IllegalStateException (e. getMessage () , e);
42 }
43 }
44
45 @Override
46 public Set <String > getElementComputeKeys () {
47 return COMPUTE_KEYS ;
48 }
49
50 @Override
51 public void setup ( final Memory memory ) {
52
53 }
54
55 @Override
56 public void execute ( final Vertex vertex , Messenger <Double >
messenger , final Memory memory ) {
57 if ( memory . isInitialIteration ()) {
58 double initialPageRank = 1.0d / this . vertexCountAsDouble
;
59 double edgeCount = Double . valueOf (( Long ) this .
messageType . edges ( vertex ). count (). next ());
60 vertex . singleProperty ( PAGE_RANK , initialPageRank );
61 vertex . singleProperty ( EDGE_COUNT , edgeCount );
62 messenger . sendMessage ( this . messageType , initialPageRank
/ edgeCount );
63 } else {
64 double newPageRank = StreamFactory . stream ( messenger .
receiveMessages ( this . messageType )). reduce (0.0d, (a,
b) -> a + b);
65 newPageRank = ( this . alpha * newPageRank ) + ((1.0 d - this
. alpha ) / this . vertexCountAsDouble );
66 vertex . singleProperty ( PAGE_RANK , newPageRank );
67 messenger . sendMessage ( this . messageType , newPageRank /
vertex .<Double > property ( EDGE_COUNT ). orElse (0.0 d));
68 }
69 }
70
71 @Override
72 public boolean terminate ( final Memory memory ) {
73 return memory . getIteration () >= this . totalIterations ;
74 }
75 }

34. Pagerank for ArangoDB
1 var pageRank = function (vertex , message , global ) {
2 var total = global . vertexCount ;
3 var edgeCount = vertex . _outEdges . length ;
4 var alpha = global . alpha ;
5 var sum = 0, rank = 0;
6 if ( global . step > 0) {
7 while ( message . hasNext ()) {
8 sum += message . next (). data ;
9 }
10 rank = alpha * sum + (1- alpha ) / total ;
11 } else {
12 rank = 1 / total ;
13 }
14 vertex . _setResult ( rank );
15 if ( global . step < global . MAX_STEPS ) {
16 var send = rank / edgeCount ;
17 while ( vertex . _outEdges . hasNext ()) {
18 message . sendTo ( vertex . _outEdges . next (). edge .
_getTarget () , send );
19 }
20 } else {
21 vertex . _deactivate ();
22 }
23 };
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35. Pregel Questions
connected components
page rank
bipartite matching
semi-clustering
mimum spanning forest
graph coloring
shortest paths
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36. Bipartite Matching
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37. Bipartite Matching
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38. Pregel Questions
connected components
page rank
bipartite matching
semi-clustering
mimum spanning forest
graph coloring
shortest paths
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39. Thank You
Twitter: @arangodb
Github: triagens/ArangoDB
Google Group: arangodb
IRC: arangodb
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