the mrnet tree-based overlay network where we’ve been, where we’re going! dorian arnold paradyn...

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The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies Group Oak Ridge National Laboratory

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Page 1: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

The MRNet Tree-based Overlay Network

Where We’ve Been,Where We’re Going!

Dorian Arnold

Paradyn ProjectUniversity of Wisconsin

Philip C. Roth

Future Technologies GroupOak Ridge National

Laboratory

Page 2: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Abstract• Large scale systems are here• Tree-based Overlay Networks (TBŌNs)

– Intuitive, seemingly restrictive– Effective model for tool scalability– Prototype: www.paradyn.org/mrnet

• Where we’ve been– Tool scalability– Programming model for large class of applications

• Where we’re going– Topology studies– TBŌNs on high-performance networks– Filters on hardware accelerators– Reliability

Page 3: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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HPC Trends from .

13

16

18

19

28

44

54

58

58

75

92

129

140

Jun-99

Nov-99

Jun-00

Nov-00

Jun-01

Nov-01

Jun-02

Nov-02

Jun-03

Nov-03

Jun-04

Nov-04

Jun-05

Nov-05

2

5

5

73

275

81

36

11

12

0 - 63

64 - 127

128 - 255

256 - 511

512 - 1023

1024 - 2047

2048 - 4095

4096 - 8191

> 8192

Growth in 1024-processor systems.November ’05

processor count distribution.

No Data Available

Easier than ever to deploy thousands of processors (one BG/L rack!)

Page 4: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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An Example: ORNL National Center for Computational Sciences

Page 5: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Hierarchical Distributed Systems

• Hierarchical Topologies– Application Control– Data collection– Data reduction/analysis

• As scale increases, front-end becomes a bottleneck

FE

BEBE BEBE…

Page 6: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs for Scalable Systems

TBŌNs for scalability– Scalable multicast

– Scalable gather

– Scalable data aggregation

FE

CPCP

CP

BEBE

CP

BEBE…

Page 7: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN ModelApplication Front-end

Application Back-ends

Tree ofCommunication Processes

FE

CPCP

CP

BEBE

CP

BEBE…

Page 8: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Model

Reliable FIFO channels– Non-lossy– Duplicate suppressing– Non-corrupting

FE

CPCP

CP

BEBE

CP

BEBE…

Page 9: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Model

FE

CPCP

CP

BEBE

CP

BEBE…

Application-level packet

Packet filter

Filter state

Channel state

Page 10: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Model

Filter function:– Inputs a packet from each child– Outputs a single packet– Updates filter state

{output, new_state } ≡ f ( inputs, cur_state )

Page 11: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs at Work• Multicast– ALMI [Pendarakis, Shi, Verma and Waldvogel ’01]– End System Multicast [Chu, Rao, Seshan and Zhang ’02]– Overcast [Jannotti, Gifford, Johnson, Kaashoek and O’Toole

’00]– RMX [Chawathe, McCanne and Brewer ’00]

• Multicast/gather (reduction)– Bistro (no reduction) [Bhattacharjee et al ’00]– Gathercast [Badrinath and Sudame ’00]– Lilith [Evensky, Gentile, Camp, and Armstrong ’97]– MRNet [Roth, Arnold and Miller ‘03]– Ygdrasil [Balle, Brett, Chen, LaFrance-Linden ’02]

• Distributed monitoring/sensing– Ganglia [Sacerdoti, Katz, Massie, Culler ’03]– Supermon (reduction) [Sottile and Minnich ’02]– TAG (reduction) [Madden, Franklin, Hellerstein and Hong

’02]

Page 12: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Example TBŌN Reductions• Simple

– Min, max, sum, count, average– Concatenate

• Complex– Clock synchronization [ Roth, Arnold, Miller ’03]

– Time-aligned aggregation [ Roth, Arnold,Miller ’03]

– Graph merging [Roth, Miller ’05]

– Equivalence relations [Roth, Arnold, Miller ‘03]– Mean-shift image segmentation [Arnold, Pack,

Miller ‘06]

Page 13: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs for Tool Scalability

MRNet integrated into Paradyn• Efficient tool startup• Performance data analysis• Scalable visualization

Page 14: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs for Scalable Applications

• Many algorithms equivalence computation– Equivalence/non-equivalence to summarize/analyze input data

• Streaming programming models• Possibly even for Bulk Synchronous Parallel programs

Application Input Filter Output

Trace Analysis Trace file Trace equivalence / Anomaly detector

Compressed traces, anomalous traces

Graph Merging Sub-graphs Sub-graph equivalence

Merged graphs

Data Clustering Data Files Object classifiers Partitioned data

Page 15: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs for Scalable Applications: Mean-Shift Algorithm

• Clustering points in feature spaces

• Useful for image segmentation

• Prohibitively expensive as feature space complexity increases

Window

Centroid

Page 16: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs for Scalable Applications: Mean-Shift Algorithm

1. Partition data into windows and calculate window densities

2. Keep windows above chosen density threshold

3. Run mean-shift on remaining windows

4. Keep local maxima as peaks

Page 17: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌNs for Scalable Applications: Mean-Shift Algorithm

• Uses MRNet as general purpose programming paradigm

• Implements mean-shift in custom MRNet filters

~6x speedup withonly 6% more nodes

Page 18: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Computational Model

• At large scales, suitable for algorithms with:– Complexity ≥ O(n), n input size

– Output size ≤ total input size*• Sometimes algorithm just runs faster on output

(better-behaved input)

– Output is in the same form as the inputs• E.g., if inputs are sets of elements, the output

should be a set of elements

Page 19: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Research and Development Directions

• TBŌN topology studies

• TBŌNs and high-performance networks

• Use of emerging technologies for TBŌN filters

• TBŌN Reliability

Page 20: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Topology

We expect many factors influence “best” topology– Physical network topology and capabilities

– Expected traffic (type and volume)

– Desired reliability guarantees

– Cost of “extra” nodes

Page 21: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Topology Investigation

• Previous studies used reasonable topologies

• How factors influence performance remains an open question

• Beginning rigorous effort to investigate this issue– Performance modeling– Empirical studies on variety of systems

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High-end Network Support

• Current MRNet implementation uses TCP/IP sockets

• Many high-end networks provide TCP/IP support– E.g., IP over Quadrics QsNet– Flexible, but undesirable for performance reasons

• Effort underway to support alternative data transports– One-sided, OS/application bypass– Complements topology investigations – Initially targeting Portals on Cray XT3

Page 23: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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High-Performance Filters on Hardware Accelerators

• Multi-paradigm computing (MPC) systems are here– MPC systems include several types of processors, such as

FPGAs, multi-core processors, GPUs, PPUs, MTA processors– E.g., Cray Adaptive Supercomputing strategy, SRC Computers,

Linux Networx, DRC FPGA co-processor

• Streaming approach expected to work well for some types

• Running filters on accelerators is natural fit for some applications, e.g. Sloan Digital Sky Survey and Large Synoptic Survey Telescope

Page 24: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Given the emergence of TBŌNs forscalable computing, low-cost

reliability for TBŌN environmentsbecomes critical!

TBŌN Reliability

1System

Size

MTTF

Page 25: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Reliability• Goal

– Tolerate process failures– Avoid checkpoint overhead

• General concept: leverage TBŌN properties– Natural information redundancies

– Computational semantics• Lost state may be replaced by non-identical state• Computational equivalence: relaxed consistency model

• Zero-cost: no additional computation, storage or network overhead during normal operation– Define operations that compensate for lost state– Maintain computational equivalence

Page 26: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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TBŌN Information Redundancies

Fundamental to the TBŌN Model

1. Input streams propagate toward root

2. Persistent state summarizes input history

3. Therefore, summary is replicated naturally as input propagates upstream

Page 27: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Recovery Strategyif failure is detected then1.Reconstruct tree

2.Regenerate compensatory state

3.Reintegrate state into tree

4.Resume normal operationend if

Page 28: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Regeneration: Composition

CPi

CPkCPj

fs( CPi )

fs( CPj ) fs( CPk )

Parent’s state iscomposition of children’s

Page 29: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Regeneration: Composition

State composition:– Input filter state from children– Output computationally-equivalent state for

parent

fs( CPi ) ≡ fs( CPj ) fs( CPk )

Child’s state Child’s stateParent’s state

CompositionOperator

Page 30: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Regeneration: Composition

Where does this mysterious composition operation come from?

When filter’s new_state is copy of output;then f becomes composition operator.

{output, new_state } ≡ f (inputs, cur_state )

Recall filter definition:

Page 31: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Regeneration: Composition

Proof Outline– State is history of processed inputs

– Children’s output becomes parent’s input

– Updated state is a copy of output• can be used as input to filter function

– Filter execution on children’s state will produce computationally equivalent state for parent

Page 32: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Regeneration: Composition

Composition can also work when output is not a copy of the state!

– Requires mapping operation from filter state to output form

Page 33: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

4

3

3

1

5

1

3

4

5

1

1

1

8

1

9

5

{ }{ }

{ }

Page 34: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

4

3

3

1

5

1

3

4

5

1

1

1

8

1

9

5

{ }{ }

{ }

Page 35: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

4

3

1

5

3

4

5

1

1

8

9

5

{1}{1,3}

{ }

{1,3} {1}

Page 36: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

3

1

3

4

1

1

9

5

{1,5,8}{1,3,4,5}

{1,3}

{1,3,4,5} {1,5,8}

{1,3}

Page 37: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

1 4 1 5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8}

{1,3,4,5} {1,5,8,9}

{1,3,4,5,8}

{1,3}

Page 38: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8,9}

{1,3,4,5} {1,5,8,9}

{1,3,4,5,8}

{1,3}

{1,3,4,5,8,9}

Page 39: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8,9}

{1,3,4,5,8}

{1,3}

{1,3,4,5,8,9}

{1,3,4,5,8,9}

Page 40: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

3

1

3

4

1

1

9

5

{1,5,8}{1,3,4,5}

{1,3}

{1,3,4,5} {1,5,8}

{1,3}

CP0 crashes!

Page 41: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

• Use f on children’s state to regenerate computationally-consistent version of lost state

CP0

CP2CP1

CP3 CP6CP4 CP5

3

1

3

4

1

1

9

5

{1,5,8}{1,3,4,5}

{1,3}

{1,3,4,5} {1,5,8}

{1,3}

fs( CP0 ) ≡ fs( CP1) fs( CP2 )

Page 42: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

3

1

3

4

1

1

9

5

{1,5,8}{1,3,4,5}

{1,3}

{1,3,4,5} {1,5,8}

{1,3}

CP0

CP2CP1

CP3 CP6CP4 CP5

3

1

3

4

1

1

9

5

{1,5,8}{1,3,4,5}

{1,3,4,5,8}

{1,3}

fs( CP0 ) ≡ fs( CP1 ) fs( CP2 )

Non-identical, but computationally-consistent!

Page 43: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

1 4 1 5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8}

{1,3,4,5} {1,5,8,9}

{1,3}

CP0

CP2CP1

CP3 CP6CP4 CP5

1 4 1 5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8}

{1,3,4,5} {1,5,8,9}

{1,3,4,5,8}

{1,3}

Page 44: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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State Composition Example

CP0

CP2CP1

CP3 CP6CP4 CP5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8,9}

{1,3,4,5} {1,5,8,9}

{1,3}

{1,3,4,5,8,9}

CP0

CP2CP1

CP3 CP6CP4 CP5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8,9}

{1,3,4,5} {1,5,8,9}

{1,3,4,5,8}

{1,3}

{1,3,4,5,8,9}

Page 45: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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CP0

CP2CP1

CP3 CP6CP4 CP5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8,9}

{1,3}

{1,3,4,5,8,9}

{1,3,4,5,8,9}

CP0

CP2CP1

CP3 CP6CP4 CP5

{1,5,8,9}{1,3,4,5}

{1,3,4,5,8,9}

{1,3,4,5,8}

{1,3}

{1,3,4,5,8,9}

{1,3,4,5,8,9}

State Composition Example

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Reliability Highlights• Zero-cost TBŌN reliability requirements:

1. Associative/commutative filter function2. Filter state and output have same

representation, or3. Known mapping from filter state

representation to output form

• Filter function used for regeneration• Many computations meet requirements

Page 47: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Other Issues• Compensating for lost messages

– Use computational state to compensate– Idempotent/non-idempotent computations

• Other state regeneration mechanisms– Decomposition

• Failure detection• Tree reconstruction• Evaluation of the recovery process

Page 48: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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MRNet References• Arnold, Pack, and Miller: “Tree-based Overlay Networks for Scalable

Applications”, Workshop on High-Level Parallel Programming Models and Supportive Environments, April 2006.

• Roth and Miller, “The Distributed Performance Consultant and the Sub-Graph Folding Algorithm: On-line Automated Performance Diagnosis on Thousands of Processes”, Principles and Practice of Parallel Programming, March 2006.

• Schulz et al, “Scalable Dynamic Binary Instrumentation for Blue Gene/L”, Workshop on Binary Instrumentation and Applications, September, 2005.

• Roth, Arnold and Miller, “Benchmarking the MRNet Distributed Tool Infrastructure: Lessons Learned”, 2004 High-Performance Grid Computing Workshop, April 2004.

• Roth, Arnold, and Miller, “MRNet: A Software-Based Multicast/Reduction Network for Scalable Tools”, SC 2003, November 2003.

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Summary• TBŌN model suitable for many types of tools,

applications and algorithms

• Future work:– Evaluation of reliability mechanisms

• Coming real soon!

– Performance modeling to support topology decisions

– TBŌNs on emerging HPC networks and technologies

– Other application areas like GIS, Bioinformatics, data mining, …

Page 50: The MRNet Tree-based Overlay Network Where We’ve Been, Where We’re Going! Dorian Arnold Paradyn Project University of Wisconsin Philip C. Roth Future Technologies

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Funding Acknowledgements• This research is sponsored in part by The National

Science Foundation under Grant EIA-0320708

• This research is also sponsored in part by the Office of Mathematical, Information, and Computational Sciences, Office of Science, U.S. Department of Energy under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC.

• Accordingly, the U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.

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EXTRA SLIDES

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MRNet Front-end Interfacefront_end_main(){ Network * net = new Network (topology_conf);

Communicator * comm = net-> get_BroadcastCommunicator();

Stream * stream = new Stream( comm, IMAX_FILT, WAITFORALL);

stream->send(“%s”, “go”);

stream->recv(“%d”, result);}

front_end_main(){ Network * net = new Network (topology_conf);

Communicator * comm = net-> get_BroadcastCommunicator();

Stream * stream = new Stream( comm, IMAX_FILT, WAITFORALL);

stream->send(“%s”, “go”);

stream->recv(“%d”, result);}

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MRNet Back-end Interface

back_end_main(){ Stream * stream; char *s;

Network * net = new Network();

net->recv(“%s”, &s, &stream);

if(s == “go”){ stream->send(“%d”, rand_int); }}

back_end_main(){ Stream * stream; char *s;

Network * net = new Network();

net->recv(“%s”, &s, &stream);

if(s == “go”){ stream->send(“%d”, rand_int); }}

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MRNet Filter Interface

imax_filter(vector<Packet> packets_in, vector<Packet> packets_out){ for( i=0; i<packets_in.size; i++){ result = max( result, packets[i].get_int()); }

Packet p(“%d”, result);

packets_out.pushback(p);}

imax_filter(vector<Packet> packets_in, vector<Packet> packets_out){ for( i=0; i<packets_in.size; i++){ result = max( result, packets[i].get_int()); }

Packet p(“%d”, result);

packets_out.pushback(p);}