6. Plenty of interest in processing them
• Graph DBMS 25% of all enterprises by 20171
• Many open-source and research prototypes on distributed
graph processing frameworks: Giraph, Pregel, GraphLab,
Chaos, GraphX, …
1Forrester Research
7. Real-world Graphs are Dynamic
Many interesting business and research insights
possible by processing them…
…but little work on incrementally updating
computation results or on window-based operations
10. A Motivating Example…
Retrieve the network state when a disruption happened
Analyze the evolution of hotspot groups in the last day by hour
Track regions of heavy load in the last 10 minutes
What factors explain the performance in the network?
11. Tegra
How do we perform efficient computations on
time-evolving, dynamically changing graphs?
12. Goals
• Create and manage time-evolving graphs
• Retrieve the network state when a disruption happened
• Temporal analytics on windows
• Analyze the evolution of hotspot groups in the last day by hour
• Sliding window computations
• Track regions of heavy load in the last 10 minutes interval
• Mix graph and data parallel computing
• What factors explain the performance in the network
14. Goals
• Create and manage time-evolving graphs using Graph
Snapshot Index
• Retrieve the network state when a disruption happened
• Temporal analytics on windows
• Analyze the evolution of hotspot groups in the last day by hour
• Sliding window computations
• Track regions of heavy load in the last 10 minutes interval
• Mix graph and data parallel computing
• What factors explain the performance in the network
16. E
D
D
A
D
C
E
C
D
A
remove add add add add
Graph Composition
Updating graphs depend on application semantics
A
B C
D
G2
A
B C
D
E
G3’
C
D
E
δg
A
+ =
17. Maintaining Multiple Snapshots
Store entire
snapshots
A
B C
G1
A
B C
D
G2
A
B C
D
E
G3
+ Efficient retrieval
- Storage overhead
Store only deltas
A
B C
δg1
A D
δg2
C
D
E
δg3
+ Efficient storage
- Retrieval overhead
18. Maintaining Multiple Snapshots
Snapshot 2Snapshot 1
t1 t2
Use a structure-sharing persistent
data-structure.
Persistent Adaptive Radix Tree (PART)
is one solution available for Spark.
19. Graph Snapshot Index
Snapshot 2Snapshot 1
Vertex
t1 t2
Snapshot 2Snapshot 1
t1 t2
Edge
Partition
Snapshot ID Management
20. Graph Windowing
A
B C
G1
A
B C
D
G2
A
B C
D
E
G3
A
C
D
E
G4
G’1= G3 G’2= G4- G1
Equivalent to GraphReduce() in GraphLINQ, GraphReduceByWindow()in CellIQ
G’2= G’1+ δg4 - δg1
G’1= δg1 + δg2 + δg3
A
B C
δg1
A D
δg2
C
D
E
δg3
B
δg4
21. Goals
• Create and manage time-evolving graphs using
Distributed Graph Snapshot Index
• Retrieve the network state when a disruption happened
• Temporal analytics on windows using Timelapse
Abstraction
• Analyze the evolution of hotspot groups in the last day by hour
• Sliding window computations
• Track regions of heavy load in the last 10 minutes interval
• Mix graph and data parallel computing
• What factors explain the performance in the network
24. Timelapse
A
B C
A
B C
D A
B C
D
E
Time
G1 G2 G3
D
BCBA
AAA
B C
D
E
• Significant reduction in messages exchanged
between graph nodes
• Avoids redundant computations
Instead, expose the temporal evolution of a node
25. Timelapse API
B C
A D
F E
A DD
B C
D
E
AA
F
B C
A D
F E
A DD
B C
D
E
AA
F
Transition
(0.977, 0.968)
(X ,Y): X is 10 iteration PageRank
Y is 23 iteration PageRank
After 11 iteration on graph 2,
Both converge to 3-digit precision
(0.977, 0.968)(0.571, 0.556)
1.224
0.8490.502
(2.33, 2.39)
2.07
0.8490.502
(0.571, 0.556)(0.571, 0.556)
8: Example showing the benefit of PSR computation.
ing master program. For each iteration of Pregel,
ck for the availability of a new graph. When it
able, we stop the iterations on the current graph,
ume resume it on the new graph after copying
e computed results. The new computation will
ve vertices in the new active set continue message
. The new active set is a function of the old active
the changes between the new graph and the old
For a large class of algorithms (e.g. incremental
nk [19]), the new active set includes vertices from
active set, any new vertices and vertices with
dditions and deletions. Listing 2 shows a simple
class Graph[V, E] {
// Collection views
def vertices(sid: Int): Collection[(Id, V)]
def edges(sid: Int): Collection[(Id, Id, E)]
def triplets(sid: Int): Collection[Triplet]
// Graph-parallel computation
def mrTriplets(f: (Triplet) => M,
sum: (M, M) => M,
sids: Array[Int]): Collection[(Int, Id, M)]
// Convenience functions
def mapV(f: (Id, V) => V,
sids: Array[Int]): Graph[V, E]
def mapE(f: (Id, Id, E) => E
sids: Array[Int]): Graph[V, E]
def leftJoinV(v: Collection[(Id, V)],
f: (Id, V, V) => V,
sids: Array[Int]): Graph[V, E]
def leftJoinE(e: Collection[(Id, Id, E)],
f: (Id, Id, E, E) => E,
sids: Array[Int]): Graph[V, E]
def subgraph(vPred: (Id, V) => Boolean,
ePred: (Triplet) => Boolean,
sids: Array[Int]): Graph[V, E]
def reverse(sids: Array[Int]): Graph[V, E]
}
Listing 3: GraphX [24] operators modified to support Tegra’s
26. Temporal Operations
Evolution analysis with no state keeping requirements
Bulk Transformations
A
B C
A
B C
D A
B C
D
E
A
B C
A
B C
D A
B C
D
E
Bulk Iterative Computations
A
B C
A
B C
D A
B C
D
E
A
A A
A
A A
A A
A A
A
A
How did the hotspots change over this window?
27. Goals
• Create and manage time-evolving graphs using
Distributed Graph Snapshot Index
• Retrieve the network state when a disruption happened
• Temporal analytics on windows using Timelapse
Abstraction
• Analyze the evolution of hotspot groups in the last day by hour
• Sliding window computations
• Track regions of heavy load in the last 10 minutes interval
• Mix graph and data parallel computing
• What factors explain the performance in the network
28. Incremental Computation
• If results from a previous snapshot is available, how can we
reuse them?
• Three approaches in the past:
• Restart the algorithm
• Redundant computations
• Memoization (GraphInc1)
• Too much state
• Operator-wise state (Naiad2,3)
• Too much overhead
1Facilitating real- time graph mining, CloudDB ’12
2 Naiad: A timely dataflow system, SOSP ’13
3 Differential dataflow, CIDR ‘13
29. Incremental Computation
A
B C
D
G1
A
B C
D
E
G2
A
B C
D A
A B
A A
A A
A
A
B C
D
E
A
A B
A
C
A
A A
A
A
Time
→ →
• Can keep state as an efficient time-evolving graph
• Not limited to vertex-centric computations
30. Incremental Computation
• Some iterative graph algorithms are robust to
graph changes
• Allow them to proceed without keeping any state
A
D E
B
C
0.5570.557
0.5570.557
2.37
A
D E
B
C B
0.5570.557
0.5570.557
2.37 0
A
D E
B
C
0.8470.507
0.8470.507
2.07 B 1.2
→
31. Goals
• Create and manage time-evolving graphs using
Distributed Graph Snapshot Index
• Retrieve the network state when a disruption happened
• Temporal analytics on windows using Timelapse
Abstraction
• Analyze the evolution of hotspot groups in the last day by hour
• Sliding window computations
• Track regions of heavy load in the last 10 minutes interval
• Mix graph and data parallel computing
• What factors explain the performance in the network
32. Implementation & Evaluation
• Implemented as a major enhancement to GraphX
• Evaluated on two open source real-world graphs
• Twitter: 41,652,230 vertices, 1,468,365,182 edges
• uk-2007: 105,896,555 vertices, 3,738,733,648 edges
36. Summary
• Processing time-evolving graph efficiently can be useful.
• Efficient storage of multiple snapshots and reducing
communication between graph nodes key to evolving graph
analysis.
37. Ongoing Work
• Expand timelapse and its incremental computation model to other
graph-parallel paradigms
• Other interesting graph algorithms:
• Fraud detection/prediction/incremental pattern matching
• Add graph querying support
• Graph queries and analytics in a single system
• Stay tuned for code release!
