Graphs, Data Mining,
and High Performance Computing
Bruce Hendrickson
Sandia National Laboratories, Albuquerque, NM
University of New Mexico, Computer Science Dept.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,
for the United States Department of Energy’s National Nuclear Security Administration
under contract DE-AC04-94AL85000.
Outline
• High performance computing
• Why current approaches can’t work for data mining
• Test case: graphs for knowledge representation
• High performance graph algorithms, an oxymoron?
• Implications for broader data mining community
• Future trends
Data Mining and High Performance Computing
• “We can only consider simple algorithms”
– Data too big for anything but O(n) algorithms
– Often have some kind of real-time constraints
• This greatly limits the kinds of questions we can address
– Terascale data gives different insights than gigascale data
– Current search capabilities are wonderful, but innately limited
• Can high-performance computing make an impact?
– What if our algorithms ran 100x faster and could use 100x more
memory? 1000x?
• Assertion: Quantitative improvements in capabilities result in
qualitative changes in the science that can be done.
Modern Computers
• Fast processors, slow memory
• Use memory hierarchy to keep processor fed
– Stage some data in smaller, faster memory (cache)
– Can dramatically enhance performance
• But only if accesses have spatial or temporal locality
– Use accessed data repeatedly, or use near-by data next
• Parallel computers are collections of these
– Pivotal to have a processor own most data it needs
• Memory patterns determine performance
– Processor speed hardly matters
High Performance Computing
• Largely the purview of science and engineering communities
– Machines, programming models, & algorithms to serve their needs
– Can these be utilized by learning and data mining communities?
– Search companies make great use of parallelism for simple things
• But not general purpose
• Goals
– Large (cumulative) core for holding big data sets
– Fast and scalable and performance of complex algorithms
– Ease of programmability
Algorithms We’ve Seen This Week
• Hashing (of many sorts)
• Feature detection
• Sampling
• Inverse index construction
• Sparse matrix and tensor products
• Training
• Clustering
• All of these involve
– complex memory access patterns
– only small amounts of computation
• Performance dominated by latency – waiting for data
Architectural Challenges
• Runtime is dominated by latency
– Lots of indirect addressing, pointer chasing, etc.
– Perhaps many at once
• Very little computation to hide memory costs
• Access pattern can be data dependent
– Prefetching unlikely to help
– Usually only want small part of cache line
• Potentially abysmal locality at all levels of memory hierarchy
– Bad serial and abysmal parallel performance
Graphs for Knowledge Representation
• Graphs can capture rich semantic structure in data
• More complex than “bag of features”
• Examples:
– Protein interaction networks
– Web pages with hyperlinks
– Semantic web
– Social networks, etc.
• Algorithms of interest include
– Connectivity (of various sorts)
– Clustering and community detection
– Common motif discovery
– Pattern matching, etc.
Semantic Graph Example
Finding Threats = Subgraph Isomorphism
Image Source:
T. Coffman,
S. Greenblatt,
S. Marcus,
Graph-based
technologies for
intelligence
analysis,
CACM, 47
(3, March 2004):
pp 45-47
Omar Khadr (at
Guantanamo)
Mohammed Jabarah (Canadian citizen
handed over to US authorities on suspicion
of links to 9/11).
Thanks to Kevin McCurley
Graph-Based Informatics: Data
• Graphs can be enormous
– High performance computing may be needed for
memory and performance
• Graphs are highly unstructured
– High variance in number of neighbors
– Little or no locality – Not partitionable
– Experience with scientific computing graphs of limited
utility
• Terrible locality in memory access patterns
Desirable Architectural Features
• Low latency / high bandwidth
– For small messages!
• Latency tolerant
• Light-weight synchronization mechanisms
• Global address space
– No data partitioning required
– Avoid memory-consuming profusion of ghost-nodes
– No local/global numbering conversions
• One machine with these properties is the Cray MTA-2
– And successor XMT
Massive Multithreading: The Cray MTA-2
• Slow clock rate (220Mhz)
• 128 “streams” per processor
• Global address space
• Fine-grain synchronization
Latency Tolerant:
important for Graph
Algorithms
• Simple, serial-like programming model
• Advanced parallelizing compilers
Cray MTA Processor
No Processor Cache!
Hashed Memory!
• Each thread can have 8 memory refs in flight
• Round trip to memory ~150 cycles
How Does the MTA Work?
• Latency tolerance via massive multi-threading
– Context switch in a single tick
– Global address space, hashed to reduce hot-spots
– No cache or local memory. Context switch on memory request.
– Multiple outstanding loads
• Remote memory request doesn’t stall processor
– Other streams work while your request gets fulfilled
• Light-weight, word-level synchronization
– Minimizes access conflicts
• Flexibly supports dynamic load balancing
• Notes:
– MTA-2 is 7 years old
– Largest machine is 40 processors
Case Study: MTA-2 vs. BlueGene/L
• With LLNL, implemented S-T shortest paths in MPI
• Ran on IBM/LLNL BlueGene/L, world’s fastest computer
• Finalist for 2005 Gordon Bell Prize
– 4B vertex, 20B edge, Erdös-Renyi random graph
– Analysis: touches about 200K vertices
– Time: 1.5 seconds on 32K processors
• Ran similar problem on MTA-2
– 32 million vertices, 128 million edges
– Measured: touches about 23K vertices
– Time: .7 seconds on one processor, .09 seconds on 10 processors
• Conclusion: 4 MTA-2 processors = 32K BlueGene/L processors
But Speed Isn’t Everything
• Unlike MTA code, MPI code limited to Erdös-Renyi graphs
– Can’t support power-law graphs; pervasive in informatics
• MPI code is 3 times larger than MTA-2 code
– Took considerably longer to develop
• MPI code can only solve this very special problem
– MTA code is part of general and flexible infrastructure
• MTA easily supports multiple, simultaneous users
• But … MPI code runs everywhere
– MTA code runs only on MTA/Eldorado and on serial machines
Multithreaded Graph Software Design
• Build generic infrastructure for core operations including…
– Breadth-first search (e.g. short paths)
– Distributed local searches (e.g. subgraph isomorphism)
– Rich filtering operations (numerous applications)
• Separate basic kernels from instance specifics
• Infrastructure is challenging to write
– Parallelization & performance challenges reside in infrastructure
– Must port to multiple architectures
• But with infrastructure in place, application development is
highly productive and portable
Customizing Behavior: Visitors
• Idea from BOOST (Lumsdaine)
• Application programmer writes small visitor functions
– Get invoked at key points by basic infrastructure
• E.g. when a new vertex is visited, etc.
– Adjust behavior or copy data; build tailored knowledge products
• Example, with one breadth-first-search routine, you can…
– Find short paths
– Construct spanning trees
– Find connected components, etc.
• Architectural dependence is hidden in infrastructure
– Applications programming is highly productive
• Use just enough C++ for flexibility, but not too much
• Note: Code runs on serial Linux, Windows, Mac machines
Eldorado Graph Infrastructure: C++ Design
Levels
Gets parallelism
for free
“Visitor”
class
Gives Parallelism,
Hides Most Concurrency
Algorithm
Class
Graph
Class
Data Str.
Class
Analyst
Support
Algorithms
Programmer
Infrastructure
Programmer
Inspired by Boost GL, but not Boost GL
Kahan’s Algorithm for Connected
Components
Infrastructure Implementation of Kahan’s
Algorithm
Kahan’s
Phase I
visitor
Kahan’s
Phase III
visitor
(Trivial)
Kahan’s
Phase II
visitor
(Trivial)
ShiloachVishkin
CRCW
(tricky)
Search
(tricky)
Infrastructure Implementation of Kahan’s
Algorithm
Phase I:
“component”
values start
“empty;”
Make them “full.”
Wait until both
“full,”
Add to hash
table
Traceview Output for Infrastructure Impl. of
Kahan’s CC algorithm
More General Filtering: The “Bully”
Algorithm
“Bully” Algorithm Implementation
Traverse “e” if we
would anyway, or if this
test returns true
Lock
dest while
testing
[or,and,replace]
Traceview Output for the Bully Algorithm
MTA-2 Scaling of Connected Components
Power Law Graph
(highly unstructured)
5.41s
2.91s
Computational Results: Subgraph
Isomorphism
A Renaissance in Architecture
• Bad news
– Power considerations limit the improvement in clock
speed
• Good news
– Moore’s Law marches on
• Real estate on a chip is no longer at a premium
– On a processor, much is already memory control
– Tiny bit is computing (e.g. floating point)
• The future is not like the past…
Example: AMD Opteron
Example: AMD Opteron
Memory
(Latency
Avoidance)
L1
D-Cache
L2
Cache
L1
I-Cache
Example: AMD Opteron
Memory
(Lat. Avoidance)
Load/Store L1
Unit
D-Cache
I-Fetch
Scan
Align
L2
Cache
L1
I-Cache
Memory Controller
Out-of-Order
Exec
Load/Store
Mem/Coherency
(Latency
Tolerance)
Example: AMD Opteron
Memory
(Latency
Avoidance)
Load/Store L1
Unit
D-Cache
Bus
HT
I-Fetch
Scan
Align
L1
I-Cache
Memory Controller
L2
Cache
DDR
Out-of-Order
Exec
Load/Store
Mem/Coherency
(Lat. Toleration)
Memory and I/O
Interfaces
Example: AMD Opteron
Memory
(Latency
Avoidance)
FPU Execution
Load/Store L1
Unit
D-Cache
HT
Int Execution Bus
I-Fetch
Scan
Align
L1
I-Cache
L2
Cache
DDR
Out-of-Order Exec
Load/Store
Mem/Coherency
(Lat. Tolerance)
Memory and I/O
Interfaces
Memory Controller
COMPUTER
Thanks to Thomas Sterling
Consequences
• Current response, stamp out more processors.
– Multicore processors. Not very imaginative.
– Makes life worse for most of us
• Near future trends
– Multithreading to tolerate latencies
– MTA-like capability on commodity machines
• Potentially big impact on data-centric applications
• Further out
– Application-specific circuitry
• E.g. hashing, feature detection, etc.
– Reconfigurable hardware?
• Adapt circuits to the application at run time
Summary
• Massive Multithreading has great potential for data mining &
learning
• Software development is challenging
– correctness
– performance
• Well designed infrastructure can hide many of these challenges
– Once built, infrastructure enables high productivity
• Potential to become mainstream. Stay tuned…
Acknowledgements
• Jon Berry
• Simon Kahan, Petr Konecny (Cray)
• David Bader, Kamesh Madduri (Ga. Tech) (MTA s-t connectivity)
• Will McClendon (MPI s-t connectivity)