Scalable Algorithms for Analysis of Massive,
Streaming Graphs
Jason Riedy, Georgia Institute of Technology;
Henning Meyerhenke, Karlsruhe Inst. of Technology;
with David Bader, David Ediger, and others at GT
15 February, 2012

Outline
Motivation
Technical
Why analyze data streams?
Overall streaming approach
Clustering coefficients
Connected components
Common aspects and questions
Session
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 2/29

Exascale Data Analysis
Health care Finding outbreaks, population epidemiology
Social networks Advertising, searching, grouping
Intelligence Decisions at scale, regulating algorithms
Systems biology Understanding interactions, drug design
Power grid Disruptions, conservation
Simulation Discrete events, cracking meshes
The data is full of semantically rich relationships.
Graphs! Graphs! Graphs!
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 3/29

Graphs are pervasive
• Sources of massive data: petascale simulations, experimental
devices, the Internet, scientific applications.
• New challenges for analysis: data sizes, heterogeneity,
uncertainty, data quality.
Astrophysics Bioinformatics Social Informatics
Problem Identifying target Problem Emergent behavior,
Problem Outlier detection
proteins information spread
Challenges Massive data
Challenges Data Challenges New analysis,
sets, temporal variation
heterogeneity, quality data uncertainty
Graph problems Matching,
Graph problems Centrality, Graph problems Clustering,
clustering
clustering flows, shortest paths
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These are not easy graphs.
Yifan Hu’s (AT&T) visualization of the Livejournal data set
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But no shortage of structure...
Protein interactions, Giot et al., “A Protein
Interaction Map of Drosophila melanogaster”,
Jason’s network via LinkedIn Labs
Science 302, 1722-1736, 2003.
• Globally, there rarely are good, balanced separators in the
scientific computing sense.
• Locally, there are clusters or communities and many levels of
detail.
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Also no shortage of data...
Existing (some out-of-date) data volumes
NYSE 1.5 TB generated daily into a maintained 8 PB archive
Google “Several dozen” 1PB data sets (CACM, Jan 2010)
LHC 15 PB per year (avg. 21 TB daily)
http://public.web.cern.ch/public/en/lhc/
Computing-en.html
Wal-Mart 536 TB, 1B entries daily (2006)
EBay 2 PB, traditional DB, and 6.5PB streaming, 17 trillion
records, 1.5B records/day, each web click is 50-150
details. http://www.dbms2.com/2009/04/30/
ebays-two-enormous-data-warehouses/
Faceboot 845 M users... and growing.
• All data is rich and semantic (graphs!) and changing.
• Base data rates include items and not relationships.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 7/29

General approaches
• High-performance static graph analysis
• Develop techniques that apply to unchanging massive graphs.
• Provides useful after-the-fact information, starting points.
• Serves many existing applications well: market research, much
bioinformatics, ...
• High-performance streaming graph analysis
• Focus on the dynamic changes within massive graphs.
• Find trends or new information as they appear.
• Serves upcoming applications: fault or threat detection, trend
analysis, ...
Both very important to different areas.
Remaining focus is on streaming.
Note: Not CS theory streaming, but analysis of streaming data.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 8/29

Why analyze data streams?
Data transfer
• 1 Gb Ethernet: 8.7TB daily at
Data volumes
100%, 5-6TB daily realistic
NYSE 1.5TB daily
• Multi-TB storage on 10GE: 300TB
LHC 41TB daily daily read, 90TB daily write
Facebook Who knows? • CPU ↔ Memory: QPI,HT:
2PB/day@100%
Data growth
Speed growth
• Facebook: > 2×/yr
• Ethernet/IB/etc.: 4× in next 2
• Twitter: > 10×/yr
years. Maybe.
• Growing sources:
• Flash storage, direct: 10× write,
Bioinformatics, 4× read. Relatively huge cost.
µsensors, security
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 9/29

Overall streaming approach
Protein interactions, Giot et al., “A Protein
Interaction Map of Drosophila melanogaster”,
Jason’s network via LinkedIn Labs
Science 302, 1722-1736, 2003.
Assumptions
• A graph represents some real-world phenomenon.
• But not necessarily exactly!
• Noise comes from lost updates, partial information, ...
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 10/29

Overall streaming approach
Protein interactions, Giot et al., “A Protein
Interaction Map of Drosophila melanogaster”,
Jason’s network via LinkedIn Labs
Science 302, 1722-1736, 2003.
Assumptions
• We target massive, “social network” graphs.
• Small diameter, power-law degrees
• Small changes in massive graphs often are unrelated.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 11/29

Overall streaming approach
Protein interactions, Giot et al., “A Protein
Interaction Map of Drosophila melanogaster”,
Jason’s network via LinkedIn Labs
Science 302, 1722-1736, 2003.
Assumptions
• The graph changes, but we don’t need a continuous view.
• We can accumulate changes into batches...
• But not so many that it impedes responsiveness.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 12/29

Difficulties for performance
• What partitioning
methods apply?
• Geometric? Nope.
• Balanced? Nope.
• Is there a single, useful
decomposition?
Not likely.
• Some partitions exist, but
they don’t often help
with balanced bisection or
memory locality.
• Performance needs new
approaches, not just
standard scientific Jason’s network via LinkedIn Labs
computing methods.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 13/29

STING’s focus
Control
action prediction
summary
Source data Simulation / query Viz
• STING manages queries against changing graph data.
• Visualization and control often are application specific.
• Ideal: Maintain many persistent graph analysis kernels.
• Keep one current snapshot of the graph resident.
• Let kernels maintain smaller histories.
• Also (a harder goal), coordinate the kernels’ cooperation.
• Gather data into a typed graph structure, STINGER.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 14/29

STINGER
STING Extensible Representation:
• Rule #1: No explicit locking.
• Rely on atomic operations.
• Massive graph: Scattered updates, scattered reads rarely
conflict.
• Use time stamps for some view of time.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 15/29

Initial results
Prototype STING and STINGER
Monitoring the following properties:
1 clustering coefficients,
2 connected components, and
3 community structure (in progress).
High-level
• Support high rates of change, over 10k updates per second.
• Performance scales somewhat with available processing.
• Gut feeling: Scales as much with sockets as cores.
http://www.cc.gatech.edu/stinger/
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Experimental setup
Unless otherwise noted
Line Model Speed (GHz) Sockets Cores
Nehalem X5570 2.93 2 4
Westmere E7-8870 2.40 4 10
• Westmere loaned by Intel (thank you!)
• All memory: 1067MHz DDR3, installed appropriately
• Implementations: OpenMP, gcc 4.6.1, Linux ≈ 3.0 kernel
• Artificial graph and edge stream generated by R-MAT
[Chakrabarti, Zhan, & Faloutsos].
• Scale x, edge factor f ⇒ 2x vertices, ≈ f · 2x edges.
• Edge actions: 7/8th insertions, 1/8th deletions
• Results over five batches of edge actions.
• Caveat: No vector instructions, low-level optimizations yet.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 17/29

Clustering coefficients
• Used to measure “small-world-ness”
[Watts & Strogatz] and potential i m
community structure
• Larger clustering coefficient ⇒ more v
inter-connected
j n
• Roughly the ratio of the number of actual
to potential triangles
• Defined in terms of triplets.
• i – v – j is a closed triplet (triangle).
• m – v – n is an open triplet.
• Clustering coefficient:
# of closed triplets / total # of triplets
• Locally around v or globally for entire graph.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 18/29

Updating triangle counts
Given Edge {u, v } to be inserted (+) or deleted (-)
Approach Search for vertices adjacent to both u and v , update
counts on those and u and v
Three methods
Brute force Intersect neighbors of u and v by iterating over each,
O(du dv ) time.
Sorted list Sort u’s neighbors. For each neighbor of v , check if in
the sorted list.
Compressed bits Summarize u’s neighbors in a bit array. Reduces
check for v ’s neighbors to O(1) time each.
Approximate with Bloom filters. [MTAAP10]
All rely on atomic addition.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 19/29

Batches of 10k actions
Brute force Bloom filter Sorted list
1.7e+04 3.4e+04 8.8e+04 1.2e+05 8.8e+04 1.4e+05
105.5
1.5e+04 1.3e+05 1.2e+05
5.1e+03 2.4e+04 2.2e+04
Updates per seconds, both metric and STINGER
3.9e+03 2.0e+04 1.7e+04 q q
q q q
q q
q
q
5 q q
q q
10 q q
qq
q
q q
q q
q
q
q Machine
104.5 q a 4 x E7−8870
q q
a 2 x X5570
q
q
q q
q
104
103.5
0 20 40 60 80 0 20 40 60 80 0 20 40 60 80
Threads
Graph size: scale 22, edge factor 16
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 20/29

Different batch sizes
Brute force Bloom filter Sorted list
105.5
105 q
q
q
q
q q
q q q q
Updates per seconds, both metric and STINGER
q q q
100
4.5 q
10 q q
q q q
q q
q q
104 q
qq q
3.5 q q
10
105.5
105 q
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1000
104.5 q
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4 x E7−8870
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2 x X5570
104 q
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103.5
105.5
q q q q
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10000
q
4.5 q
10 q q
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q
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104
103.5
0 20 40 60 80 0 20 40 60 80 0 20 40 60 80
Threads
Graph size: scale 22, edge factor 16
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 21/29

Different batch sizes: Reactivity
Brute force Bloom filter Sorted list
100
10−0.5
Seconds between updates, both metric and STINGER
10−1
100
q
qq
10−1.5 q
q
q
q
q q
10−2 q
q q
q q
q q
q q
q
10−2.5 q
q q q
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q q q
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10−3 q q
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100
10−0.5 q
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q Machine
10−1 qq
1000
q
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q 4 x E7−8870
10−1.5 q
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10−2
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10−2.5
10−3
100 q q
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10−0.5 q
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10−1 qq qqq
10000
q q q q q
q q q
q q q
10−1.5
10−2
10−2.5
10−3
0 20 40 60 80 0 20 40 60 80 0 20 40 60 80
Threads
Graph size: scale 22, edge factor 16
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 22/29

Connected components
• Maintain a mapping from vertex to
component.
• Global property, unlike triangle
counts
• In “scale free” social networks:
• Often one big component, and
• many tiny ones.
• Edge changes often sit within
components.
• Remaining insertions merge
components.
• Deletions are more difficult...
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 23/29

Connected components
• Maintain a mapping from vertex to
component.
• Global property, unlike triangle
counts
• In “scale free” social networks:
• Often one big component, and
• many tiny ones.
• Edge changes often sit within
components.
• Remaining insertions merge
components.
• Deletions are more difficult...
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 24/29

Connected components: Deleted edges
The difficult case
• Very few deletions
matter.
• Determining which
matter may require a
large graph search.
• Re-running static
component
detection.
• (Long history, see
related work in
[MTAAP11].)
• Coping mechanisms:
• Heuristics.
• Second level of
batching.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 25/29

Deletion heuristics
Rule out effect-less deletions
• Use the spanning tree by-product of static connected
component algorithms.
• Ignore deletions when one of the following occur:
1 The deleted edge is not in the spanning tree.
2 If the endpoints share a common neighbor∗ .
3 If the loose endpoint can reach the root∗ .
• In the last two (∗), also fix the spanning tree.
Rules out 99.7% of deletions.
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 26/29

Connected components: Performance
106 2.4e+03 1.6e+04 6.4e+03
3.2e+03 2.0e+03
105
100
Updates per seconds, both metric and STINGER
104
103
106 1.7e+04 7.7e+04 1.4e+04
1.9e+04 2.0e+04
105 Machine
1000
104
a 4 x E7−8870
a 2 x X5570
3
10
106 5.8e+04 1.3e+05 1.5e+05
5.5e+04 1.1e+05
5
10
10000
104
103
12 4 6 8 12 16 24 32 40 48 56 64 72 80
Threads
Graph size: scale 22, edge factor 16
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 27/29

Common aspects
• Each parallelizes sufficiently well over the affected vertices V ,
those touched by new or removed edges.
• Total amount of work is O(Vol(V )) = O( v ∈V deg(v )).
• Our in-progress work on refining or re-agglomerating
communities with updates also is O(Vol(V )).
• How many interesting graph properties can be updated with
O(Vol(V )) work?
• Do these parallelize well?
• The hidden constant and how quickly performance becomes
asymptotic determines the metric update rate. What
implementation techniques bash down the constant?
• How sensitive are these metrics to noise and error?
• How quickly can we “forget” data and still maintain metrics?
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 28/29

Session outline
Emergent Behavior Detection in Massive Graphs :
Nadya Bliss and Benjamin Miller, Massachusetts
Institute of Technology, USA
Scalable Graph Clustering and Analysis with KDT :
John R. Gilbert and Adam Lugowski, University of
California, Santa Barbara, USA; Steve Reinhardt, Cray,
USA
Multiscale Approach for Network Compression-friendly Ordering :
Ilya Safro, Argonne National Laboratory, USA; Boris
Temkin, Weizmann Institute of Science, Israel
SIAM PP 2012—Scalable Algorithms for Analysis of Massive, Streaming Graphs—Jason Riedy 29/29

Acknowledgment of support
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