Gradoop is a framework for large-scale graph analytics based on Apache Flink. The talk was given at the Flink Forward Conference 2015 in Berlin.

1. GRADOOP: Scalable Graph
Analytics with Apache Flink
Martin Junghanns
University of Leipzig

2. About the speaker and the team
 2011 Bachelor of Engineering
 Thesis: Partitioning of Dynamic Graphs
 2014 Master of Science
 Thesis: Graph Database Systems for Business Intelligence
 Now: PhD Student, Database Group, University of Leipzig
 Distributed Systems
 Distributed Graph Data Management
 Graph Theory & Algorithms
 Professional Experience: sones GraphDB, SAP
André, PhD Student
Martin, PhD Student
Kevin, M.Sc. StudentNiklas, M.Sc. Student

3. Motivation

4. 𝑮𝑟𝑟𝑟𝑟 = (𝑽𝑒𝑒𝑒𝑒𝑒𝑒𝑒, 𝑬𝑑𝑑𝑑𝑑)
“Graphs are everywhere”

5. 𝐺𝐺𝐺𝐺𝐺 = (𝐔𝐔𝐔𝐔𝐔, 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹)
“Graphs are everywhere”
Alice
Bob
Eve
Dave
Carol
Mallory
Peggy

6. 𝐺𝐺𝐺𝐺𝐺 = (𝐔𝐔𝐔𝐔𝐔, 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹)
“Graphs are everywhere”
Alice
Bob
Eve
Dave
Carol
Mallory
Peggy

7. 𝐺𝐺𝐺𝐺𝐺 = (𝐔𝐔𝐔𝐔𝐔, 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹)
“Graphs are everywhere”
Alice
Bob
Eve
Dave
Carol
Mallory
Peggy

8. 𝐺𝐺𝐺𝐺𝐺 = (𝐔𝐔𝐔𝐔𝐔, 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹)
“Graphs are everywhere”
Alice
Bob
Eve
Dave
Carol
Mallory
Peggy

9. 𝐺𝐺𝐺𝐺𝐺 = (𝐔𝐔𝐔𝐔𝐔, 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹)
“Graphs are everywhere”
Alice
Bob
Eve
Dave
Carol
Mallory
Peggy
Trent

10. 𝐺𝐺𝐺𝐺𝐺 = (𝐔𝐔𝐔𝐔𝐔, 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹)
“Graphs are everywhere”
Alice
Bob
Eve
Dave
Carol
Mallory
Peggy
Trent

11. 𝐺𝐺𝐺𝐺𝐺 = (𝐂𝐂𝐂𝐂𝐂𝐂, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶)
“Graphs are everywhere”
Leipzig
pop: 544K
Dresden
pop: 536K
Berlin
pop: 3.5M
Hamburg
pop: 1.7M
Munich
pop: 1.4M
Chemnitz
pop: 243K
Nuremberg
pop: 500K
Cologne
pop: 1M

12.  World Wide Web
 ca. 1 billion websites
“Graphs are large”
 Facebook
 ca. 1.49 billion active users
 ca. 340 friends per user

13. End-to-End Graph Analytics
Data Integration Graph Analytics Representation

14. End-to-End Graph Analytics
Data Integration Graph Analytics Representation
 Integrate data from one or more sources into a dedicated
graph storage with common graph data model

15. End-to-End Graph Analytics
Data Integration Graph Analytics Representation
 Integrate data from one or more sources into a dedicated
graph storage with common graph data model
 Definition of analytical workflows from operator algebra

16. End-to-End Graph Analytics
Data Integration Graph Analytics Representation
 Integrate data from one or more sources into a dedicated
graph storage with common graph data model
 Definition of analytical workflows from operator algebra
 Result representation in a meaningful way

17. Graph Data Management
Graph Database
Systems
Neo4j, OrientDB
Graph Processing
Systems
Pregel, Giraph
Distributed Workflow
Systems
Flink Gelly, Spark GraphX
Data Model Rich Graph
Models
Generic Graph Models Generic Graph Models
Focus Local ACID
Operations
Global Graph Operations Global Data and Graph
Operations
Query Language Yes No No
Persistency Yes No No
Scalability Vertical Horizontal Horizontal
Workflows No No Yes
Data Integration No No No
Graph Analytics No Yes Yes
Representation Yes No No

18. Graph Data Management
Graph Database
Systems
Neo4j, OrientDB
Graph Processing
Systems
Pregel, Giraph
Distributed Workflow
Systems
Flink Gelly, Spark GraphX
Data Model Rich Graph
Models
Generic Graph Models Generic Graph Models
Focus Local ACID
Operations
Global Graph Operations Global Data and Graph
Operations
Query Language Yes No No
Persistency Yes No No
Scalability Vertical Horizontal Horizontal
Workflows No No Yes
Data Integration No No No
Graph Analytics No Yes Yes
Representation Yes No No

19. Graph Data Management
Graph Database
Systems
Neo4j, OrientDB
Graph Processing
Systems
Pregel, Giraph
Distributed Workflow
Systems
Flink Gelly, Spark GraphX
Data Model Rich Graph
Models
Generic Graph Models Generic Graph Models
Focus Local ACID
Operations
Global Graph Operations Global Data and Graph
Operations
Query Language Yes No No
Persistency Yes No No
Scalability Vertical Horizontal Horizontal
Workflows No No Yes
Data Integration No No No
Graph Analytics No Yes Yes
Representation Yes No No

20. Graph Data Management
Graph Database
Systems
Neo4j, OrientDB
Graph Processing
Systems
Pregel, Giraph
Distributed Workflow
Systems
Flink Gelly, Spark GraphX
Data Model Rich Graph
Models
Generic Graph Models Generic Graph Models
Focus Local ACID
Operations
Global Graph Operations Global Data and Graph
Operations
Query Language Yes No No
Persistency Yes No No
Scalability Vertical Horizontal Horizontal
Workflows No No Yes
Data Integration No No No
Graph Analytics No Yes Yes
Representation Yes No No

21. What‘s missing?
An end-to-end framework and research platform
for efficient, distributed and domain independent
graph data management and analytics.

22. What‘s missing?
An end-to-end framework and research platform
for efficient, distributed and domain independent
graph data management and analytics.

23. Gradoop Architecture & Data Model

24. High Level Architecture
HDFS/YARN
Cluster
HBase Distributed Graph Store
Extended Property Graph Model
Flink Operator Implementations
Data Integration
Flink Operator Execution
Workflow
Declaration
Visual
GrALa DSL
Representation
Data flow
Control flow
Graph Analytics Representation
Workflow Execution

25. High Level Architecture
HBase Distributed Graph Store
Extended Property Graph Model
Flink Operator Implementations
Data Integration
Flink Operator Execution
Workflow
Declaration
Visual
GrALa DSL
Representation
Data flow
Control flow
Graph Analytics Representation
Workflow Execution
HDFS/YARN
Cluster

26. Extended Property Graph Model

27. Extended Property Graph Model

28. Extended Property Graph Model

29. Graph Operators
Operator GrALa notation
Binary
Combination graph.combine(otherGraph) : Graph
Overlap graph.overlap(otherGraph) : Graph
Exclusion graph.exclude(otherGraph) : Graph
Isomorphism graph.isIsomorphicTo(otherGraph) : Boolean
Unary
Pattern Matching graph.match(patternGraph,predicate) : Collection
Aggregation graph.aggregate(propertyKey,aggregateFunction) : Graph
Projection graph.project(vertexFunction,edgeFunction) : Graph
Summarization graph.summarize(
vertexGroupKeys,vertexAggregateFunction,
edgeGroupKeys,edgeAggregateFunction) : Graph

30. Combination
1: personGraph = db.G[0].combine(db.G[1]).combine(db.G[2])

31. Combination
1: personGraph = db.G[0].combine(db.G[1]).combine(db.G[2])

32. Graph Operators
Operator GrALa notation
Binary
Combination graph.combine(otherGraph) : Graph
Overlap graph.overlap(otherGraph) : Graph
Exclusion graph.exclude(otherGraph) : Graph
Isomorphism graph.isIsomorphicTo(otherGraph) : Boolean
Unary
Pattern Matching graph.match(patternGraph,predicate) : Collection
Aggregation graph.aggregate(propertyKey,aggregateFunction) : Graph
Projection graph.project(vertexFunction,edgeFunction) : Graph
Summarization graph.summarize(
vertexGroupKeys,vertexAggregateFunction,
edgeGroupKeys,edgeAggregateFunction) : Graph

33. Summarization
1: personGraph = db.G[0].combine(db.G[1]).combine(db.G[2])
2: vertexGroupingKeys = {:type, “city”}
3: edgeGroupingKeys = {:type}
4: vertexAggFunc = (Vertex vSum, Set vertices => vSum[“count”] = |vertices|)
5: edgeAggFunc = (Edge eSum, Set edges => eSum[“count”] = |edges|)
6: sumGraph = personGraph.summarize(vertexGroupingKeys, vertexAggFunc,
edgeGroupingKeys, edgeAggFunc)

34. Summarization
1: personGraph = db.G[0].combine(db.G[1]).combine(db.G[2])
2: vertexGroupingKeys = {:type, “city”}
3: edgeGroupingKeys = {:type}
4: vertexAggFunc = (Vertex vSum, Set vertices => vSum[“count”] = |vertices|)
5: edgeAggFunc = (Edge eSum, Set edges => eSum[“count”] = |edges|)
6: sumGraph = personGraph.summarize(vertexGroupingKeys, vertexAggFunc,
edgeGroupingKeys, edgeAggFunc)

35. Graph Collection Operators
Operator GrALa notation
Collection
Selection collection.select(predicate) : Collection
Distinct collection.distinct() : Collection
Sort by collection.sortBy(key, [:asc|:desc]) : Collection
Top collection.top(limit) : Collection
Union collection.union(otherCollection) : Collection
Intersection collection.intersect(otherCollection) : Collection
Difference collection.difference(otherCollection) : Collection
Auxiliary
Apply collection.apply(unaryGraphOperator) : Collection
Reduce collection.reduce(binaryGraphOperator) : Graph
Call [graph|collection].callFor[Graph|Collection](
algorithm,parameters) : [Graph|Collection]

36. Selection
1: collection = <db.G[0],db.G[1],db.G[2]>
2: predicate = (Graph g => |g.V| > 3)
3: result = collection.select(predicate)

37. Selection
1: collection = <db.G[0],db.G[1],db.G[2]>
2: predicate = (Graph g => |g.V| > 3)
3: result = collection.select(predicate)

38. Graph Collection Operators
Operator GrALa notation
Collection
Selection collection.select(predicate) : Collection
Distinct collection.distinct() : Collection
Sort by collection.sortBy(key, [:asc|:desc]) : Collection
Top collection.top(limit) : Collection
Union collection.union(otherCollection) : Collection
Intersection collection.intersect(otherCollection) : Collection
Difference collection.difference(otherCollection) : Collection
Auxiliary
Apply collection.apply(unaryGraphOperator) : Collection
Reduce collection.reduce(binaryGraphOperator) : Graph
Call [graph|collection].callFor[Graph|Collection](
algorithm,parameters) : [Graph|Collection]

39. Extended Property Graph Model in Flink
ID Label Properties Graphs
ID Label Properties Source
Vertex
Target
Vertex
Graphs
VertexData
EdgeData
GraphData
ID Label Properties
POJO
POJO
POJO
DataSet<Vertex<ID,VertexData>>
DataSet<Edge<ID,EdgeData>>
DataSet<Subgraph<ID,GraphData>>
Gelly
𝒱
ℰ
𝒢
Pojo Representation

40. Extended Property Graph Model in Flink
VertexData
EdgeData
GraphData
POJO
POJO
POJO
DataSet<Vertex<ID,VertexData>>
DataSet<Edge<ID,EdgeData>>
DataSet<Subgraph<ID,GraphData>>
Gelly
VertexData
EdgeData
GraphData
Tuple
Tuple
Tuple
DataSet<VertexData>
DataSet<EdgeData>
DataSet<GraphData>
𝒱
𝒱
ℰ
ℰ
𝒢
𝒢
Pojo Representation
Tuple Representation
ID Label Properties Graphs
ID Label Properties Source
Vertex
Target
Vertex
Graphs
ID Label Properties
ID Label Properties Graphs
ID Label Properties Source
Vertex
Target
Vertex
Graphs
ID Label Properties

41. Summarization in Flink
VID City
0 L
1 L
2 D
3 D
4 D
5 B
EID S T
0 0 1
1 1 0
2 1 2
3 2 1
4 2 3
5 3 2
6 4 0
7 4 1
8 5 2
9 5 3
L [0,1]
D [2,3,4]
B [5]
VID City Count
0 L 2
2 D 3
5 B 1
VID Rep
0 0
1 0
2 2
3 2
4 2
5 5
ID S T
0 0 1
1 0 0
2 0 2
3 2 1
4 2 3
5 2 2
6 2 0
7 2 1
8 5 2
9 5 3
ID S T
0 0 0
1 0 0
2 0 2
3 2 0
4 2 2
5 2 2
6 2 0
7 2 0
8 5 2
9 5 2
0,0 [0,1]
0,2 [2]
2,0 [3,6,7]
2,2 [4,5]
5,2 [8,9]
EID S T Count
0 0 1 2
2 0 2 1
3 2 0 3
4 2 2 2
8 5 2 2
join(VID==S)
𝒱
ℰ’
𝒱′
ℰ
groupBy(City)
reduceGroup + filter + map
reduceGroup + filter + map
groupBy(S,T)
join(VID==T)

42. Use Case: Graph Business Intelligence

43. Use Case: Graph Business Intelligence
 Business intelligence usually based on relational data
warehouses
 Enterprise data is integrated within dimensional schema
 Analysis limited to predefined relationships
 No support for relationship-oriented data mining
Facts
Dim 1
Dim 2
Dim 3

44. Use Case: Graph Business Intelligence
 Business intelligence usually based on relational data
warehouses
 Enterprise data is integrated within dimensional schema
 Analysis limited to predefined relationships
 No support for relationship-oriented data mining
 Graph-based approach
 Integrate data sources within an instance graph by preserving original
relationships between data objects (transactional and master data)
 Determine subgraphs (business transaction graphs) related to business
activities
 Analyze subgraphs or entire graphs with aggregation queries, mining
relationship patterns, etc.
Facts
Dim 1
Dim 2
Dim 3

45. Prerequisites: Data Integration

46. Business Transaction Graphs
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
basedOn serves
serves
bills
bills
bills
processedBy

47. Business Transaction Graphs
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

48. Business Transaction Graphs
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

49. Business Transaction Graphs
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

50. Business Transaction Graphs
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

51. Business Transaction Graphs
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

52. BTG 1
(1) BTG Extraction
BTG 2
BTG 3
BTG 4
BTG 5
BTG n
…

53. (1) BTG Extraction
// generate base collection
btgs = iig.callForCollection( :BusinessTransactionGraphs , {} )

54. (2) Profit Aggregation
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

55. (2) Profit Aggregation
// generate base collection
btgs = iig.callForCollection( :BusinessTransactionGraphs , {} )
// define profit aggregate function
aggFunc = ( Graph g =>
g.V.values(“Revenue").sum() - g.V.values(“Expense").sum()
)

56. (2) Profit Aggregation
BTG 1
BTG 2
BTG 3
BTG 4
BTG 5
BTG n
… ∑ Revenue ∑ Expenses Net Profit
5,000 -3,000 2,000
9,000 -3,000 6,000
2,000 -1,500 500
5,000 -7,000 -2,000
10,000 -15,000 -5,000
… … …
8,000 -4,000 4,000

57. (2) Profit Aggregation
// generate base collection
btgs = iig.callForCollection( :BusinessTransactionGraphs , {} )
// define profit aggregate function
aggFunc = ( Graph g =>
g.V.values(“Revenue").sum() - g.V.values(“Expense").sum()
)
// apply aggregate function and store result at new property
btgs = btgs.apply( Graph g =>
g.aggregate( “Profit“ , aggFunc )
)

58. (3) BTG Clustering
BTG 1
BTG 2
BTG 3
BTG 4
BTG 5
BTG n
… ∑ Revenue ∑ Expenses Net Profit
5,000 -3,000 2,000
9,000 -3,000 6,000
2,000 -1,500 500
5,000 -7,000 -2,000
10,000 -15,000 -5,000
… … …
8,000 -4,000 4,000

59. (3) BTG Clustering
// select profit and loss clusters
profitBtgs = btgs.select( Graph g => g[“Profit”] >= 0 )
lossBtgs = btgs.difference(profitBtgs)

60. (4) Cluster Characteristic Patterns
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

61. (4) Cluster Characteristic Patterns
CIT ERP
Employee
Name: Dave
Employee
Name: Alice
Employee
Name: Bob
Employee
Name: Carol
Ticket
Expense: 500
SalesQuotation
SalesOrder
PurchaseOrder
PurchaseOrder
SalesRevenue
Revenue: 5,000
PurchaseInvoice
Expense: 2,000
PurchaseInvoice
Expense: 1,500
sentBy
createdBy
processedBy
createdBy
openedFor
processedBy
processedBy
basedOn serves
serves
bills
bills
bills

62. (4) Cluster Characteristic Patterns
BTG 1
BTG 2
BTG 3
BTG 4
BTG 5
BTG n
…
∑ Revenue ∑ Expenses Net Profit
5,000 -3,000 2,000
9,000 -3,000 6,000
2,000 -1,500 500
5,000 -7,000 -2,000
10,000 -15,000 -5,000
… … …
8,000 -4,000 4,000
TicketAlice
processedBy
Bob
createdBy
PurchaseOrder

63. (4) Cluster Characteristic Patterns
// select profit and loss clusters
profitBtgs = btgs.select( Graph g => g[“Profit”] >= 0 )
lossBtgs = btgs.difference(profitBtgs)
// apply magic
profitFreqPats = profitBtgs.callForCollection(
:FrequentSubgraphs , {“Threshold”:0.7}
)
lossFreqPats = lossBtgs.callForCollection(
:FrequentSubgraphs , {“Threshold”:0.7}
)
// determine cluster characteristic patterns
trivialPats = profitFreqPats.intersect(lossFreqPats)
profitCharPatterns = profitFreqPats.difference(trivialPats)
lossCharPatterns = lossFreqPats.difference(trivialPats)

64. Current State & Future Work

65. Current State
 0.0.1 First Prototype (May 2015)
 Hadoop MapReduce and Giraph for operator implementations
 Too much complexity
 Performance loss through serialization in HDFS/HBase
 0.0.2 Using Flink as execution layer (June 2015)
 Basic operators
 Currently 0.0.3-SNAPSHOT
 Performance improvements
 More operator implementations

66. Operator implementations (0.0.3-SNAPSHOT)
Unary Pattern Matching Collection Selection Algorithms LabelPropagation
Aggregation Distinct BTG Extraction
Projection Sort by FSM
Summarization Top
Binary Combination Union
Overlap Intersection
Exclusion Difference
Isomorphism Auxiliary Apply
Reduce
Call

67. Future Work
 Operator integration into Gelly
 Summarization FLINK-2411
 Graph Sampling
 …
 Graph Operations on streams (Flink)
 Graph Partitioning (maybe together with the Gelly people)
 Graph Versioning (Storage)
 Benchmarking
 GrALa Interpreter / Web UI

68. Benchmarks Sneak Preview
0
200
400
600
800
1000
1200
1400
1 2 4 8 16
Time [s]
# Worker
Summarization (Vertex and Edge Labels)
 16x Intel(R) Xeon(R) CPU E5-2430 v2 @ 2.50GHz (12 Cores), 48 GB RAM
 Hadoop 2.5.2, Flink 0.9.0
 slots (per node) 12
 jobmanager.heap.mb 2048
 taskmanager.heap.mb 40960
 Foodbroker Graph (https://github.com/dbs-leipzig/foodbroker)
 Generates BI process data
 858,624,267 Vertices, 4,406,445,007 Edges, 663GB Payload

69. Web UI Sneak Preview

70. Contributions welcome
 Code
 Operator implementations
 Performance Tuning
 Storage layout
 Data! and Use Cases
 We are researchers, we assume ...
 Getting real data (especially BI data) is nearly impossible
 People
 Bachelor / Master / PhD Thesis

71. Thank you for building Flink!
www.gradoop.com
https://github.com/dbs-leipzig/gradoop
http://dbs.uni-leipzig.de/file/GradoopTR.pdf
http://dbs.uni-leipzig.de/file/biiig-vldb2014.pdf