Processing large-scale graphs with Google Pregel

Processing large-scale graphs
with GoogleTMPregel
Max Neunhöﬀer
Big data technology and applications, 25 March 2015
www.arangodb.com

About
about me
Max Neunhöﬀer (@neunhoef) working for ArangoDB

About
about me
Max Neunhöﬀer (@neunhoef) working for ArangoDB
about the talk
diﬀerent kinds of graph algorithms
Pregel example
Pregel mind set
ArangoDB implementation

Graph Algorithms
Pattern matching
Search through the entire graph
Identify similar components
⇒ Touch all vertices and their neighbourhoods

Graph Algorithms
Pattern matching
Traversals
Deﬁne a speciﬁc start point
Iteratively explore the graph
⇒ History of steps is known

Graph Algorithms
Pattern matching
Traversals
Deﬁne a speciﬁc 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

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 traﬃc
Good at calculations touching all vertices
Bad at calculations touching a very small number of vertices

Example – Connected Components
active inactive
3 forward message 2 backward message
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active inactive
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active inactive
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active inactive
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active inactive
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active inactive
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Worker ˆ= Map
“Map” a user-deﬁned algorithm over all vertices
Output: set of messages to other vertices
Available parameters:
The current vertex and its outbound edges
All incoming messages
Global values
Allow modiﬁcations on the vertex:
Attach a result to this vertex and its outgoing edges
Delete the vertex and its outgoing edges
Deactivate the vertex

Combine ˆ= 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 traﬃc

Activity ˆ= 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

The Multi-Model Approach
Multi-model database
A multi-model database combines a document store with a
graph database and is at the same time a key/value store,

with a common query language for all three data models.

Important:
is able to compete with specialised products on their turf

Important:
is able to compete with specialised products on their turf
allows for polyglot persistence using a single database

is a multi-model database (document store & graph database),

is open source and free (Apache 2 license),

oﬀers convenient queries (via HTTP/REST and AQL),

including joins between diﬀerent collections,

conﬁgurable consistency guarantees using transactions

memory eﬃcient by shape detection,

uses JavaScript throughout (Google’s V8 built into server),

API extensible by JS code in the Foxx Microservice Framework,

oﬀers many drivers for a wide range of languages,

is easy to use with web front end and good documentation,

is easy to use with web front end and good documentation,
and enjoys good community as well as professional support.

Extensible through JavaScript
The Foxx Microservice Framework
Allows you to extend the HTTP/REST API by your own
routes, which you implement in JavaScript running on the
database server, with direct access to the C++ DB engine.

Unprecedented possibilities for data centric services:
custom-made complex queries or authorizations

schema-validation

schema-validation
push feeds, etc.

Pregel in ArangoDB
Started as a side project in free hack time
Experimental on operational database
Implemented as an alternative to traversals
Make use of the ﬂexibility of JavaScript:
No strict type system
No pre-compilation, on-the-ﬂy queries
Native JSON documents
Really fast development

Cluster structure of ArangoDB
Requests
DBserver DBserver DBserver
CoordinatorCoordinator
4 2 5 3 11

Pagerank for Giraph
1 public class SimplePageRankComputation extends BasicComputation <
LongWritable , DoubleWritable , FloatWritable , DoubleWritable >
{
2 public static final int MAX_SUPERSTEPS = 30;
3
4 @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 ((0.15f /
getTotalNumVertices ()) + 0.85f * 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() * 100f;
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 }

Pagerank for TinkerPop3
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 = 0.85d;
11 private int totalIterations = 30;
12 private static final Set <String > COMPUTE_KEYS = new HashSet <>(
Arrays.asList(PAGE_RANK , EDGE_COUNT));
13
14 private PageRankVertexProgram () {}
15
16 @Override
17 public void loadState(final Configuration configuration) {
18 this.vertexCountAsDouble = configuration.getDouble(
VERTEX_COUNT , 1.0d);
19 this.alpha = configuration.getDouble(ALPHA , 0.85d);
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) + ((1.0d - this
.alpha) / this.vertexCountAsDouble);
66 vertex.singleProperty(PAGE_RANK , newPageRank);
67 messenger.sendMessage(this.messageType , newPageRank /
vertex.<Double >property(EDGE_COUNT).orElse (0.0d));
68 }
69 }
70
71 @Override
72 public boolean terminate(final Memory memory) {
73 return memory.getIteration () >= this.totalIterations;
74 }
75 }

Pagerank for ArangoDB
1 var pageRank = function (vertex , message , global) {
2 var total , rank , edgeCount , send , edge , alpha , sum;
3 total = global.vertexCount;
4 edgeCount = vertex._outEdges.length;
5 alpha = global.alpha;
6 sum = 0;
7 if (global.step > 0) {
8 while (message.hasNext ()) {
9 sum += message.next().data;
10 }
11 rank = alpha * sum + (1-alpha) / total;
12 } else {
13 rank = 1 / total;
14 }
15 vertex._setResult(rank);
16 if (global.step < global.MAX_STEPS) {
17 send = rank / edgeCount;
18 while (vertex._outEdges.hasNext ()) {
19 edge = vertex._outEdges.next();
20 message.sendTo(edge._getTarget (), send);
21 }
22 } else {
23 vertex._deactivate ();
24 }
25 };
26
27 var combiner = function (message , oldMessage) {
28 return message + oldMessage;
29 };
30
31 var Runner = require ("org/arangodb/pregelRunner ").Runner;
32 var runner = new Runner ();
33 runner.setWorker(pageRank);
34 runner.setCombiner(combiner);
35 runner.setGlobal (" alpha", 0.85);
36 runner.setGlobal (" vertexCount", db.vertices.count ());
37 runner.start (" myGraph ");

Pregel-type problems
page rank
single-source shortest paths (all)
maximal bipartite matching (randomized)
semi-clustering
connected components
distributed minimum spanning forest
graph coloring

Thanks
Twitter: @arangodb @neunhoef
Github: ArangoDB/ArangoDB
Google Group: arangodb
IRC: arangodb
https://www.arangodb.com

Processing large-scale graphs with Google Pregel

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