PREDIcT: Towards Predicting the Runtime of Iterative Analytics

Adrian Popescu1, Andrey Balmin2, Vuk Ercegovac3, Anastasia Ailamaki1

1 2 3

Predicting Runtime of Iterative Analytics

2

computation messaging synch

Requirements:• # of iterations• per iteration resources (key features), i.e.,

for Bulk Synchronous Parallel (BSP):

• cost model

Challenges:• dependence on prior iterations• variable resource requirements

Tim

e Ite

ratio

n 1

Workers

Tim

e Ite

ratio

n 2

Partitioned Input

PREDIcT at a Glance

3• Cost model for BSP Execution Model

Reso

urc

es

Iterations

Sample run

Iterations

Actual run

Reso

urc

es

• Transformations: • Input dataset: sampling• Parameters: transform function

• Prediction methodology for iterative analytics on graphs:

Proportionality for resources,similarity for # of iterations

Supported AnalyticsGlobal convergence metric: e.g., an average, a ratio, fix point



Ranking (e.g., PageRank)

Graph processing (e.g., neighborhood estimation)

Graph clustering (e.g., semi-clustering)

Example: PageRank

⇒ Sampling technique

⇒ Transform function



• PageRank of a page: given by the rank of its inbound pages

• Rank computation: iterative

• Convergence: RankChange < τG1. graph structure:

connectivity, degree ratio, diameter

2. parameters: N, τG

1

2 4

3

8

7

6

5G

Sampling: Biased Random Jump

• Variation of Random Jump (RJ) / random walk

Sampling scale-free graphs: e.g., web graphs

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RJ BRJ

• Seed vertices: k high out degree nodes (hubs)

G

Disconnected Connected sampleBRJ: Improving connectivity at the same sampling ratio

Transformations: Preserving Iterations

1 3

8

5S Sampling Ratio (SR) = 50%

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2 4

3

8

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6

5G

Convergence: RankChange (G) < τG



τS = τG / SR

Average rank change: RankChange(S) prop. w/ RankChange(G)Transform function T:

Sample and transform function preserve iterations

S maintains: connectivity, in/out degree ratio, effective diameter

Prediction

Cost ModelF (X1,…,Xk)

Extrapolator

Runtime

Scaled features

Profiled features

Sample run Estimated actual run

Two extrapolation factors:• on edges• on vertices

Customized cost model for the Bulk Synchronous Parallel execution model: i.e., Giraph BSP



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Tim

e Ite

ratio

n 1

Workers

Partitioned Input

Cost Model: Translating Features into Time

Active vertices, message counts

Message counts / sizes,Locality of messages

Skew

computation messaging synch

• Each phase but synch: multivariate linear

regression

• Synchronization: identifying critical path

Bulk Synchronous Parallel Model

Experimental Evaluation• Setup: 10 machines, 6C CPUs Intel X5660, 48GB

RAM, 1Gbps

• Datasets: Real graph datasets: Wikipedia (Wiki), Twitter (TW), UK-2002 (UK), LiveJournal(LJ), with sizes in [1,25] GB

• Representative Algorithms: PageRank (PR), Top-k Ranking and semi-clustering (SC)

• Default transformations: BRJ and Tr = (IDConf, τS = τG / SR)

• Metrics: signed relative error: RE=(Predicted - Actual) * 100 % / Actual (i.e., “+” = over-prediction, “-” = under-prediction) 10

Predicting Features (Iterations)Giraph BSP, 10 machines, real datasets in [1,25] GB



Predicting Features (Iterations)

Predicting iterations for semi-clustering: Ϯ= 0:01(left), and Ϯ = 0:001 (right).

Predicting Features (Iterations)

Predicting key features for top-k ranking: Predicting iterations (left), and predicting remote message bytes (right).

Predicting Features (Iterations)

LJ Wiki UK-2002 Twitter0

13

25

38

50Actual UpBound PREDIcT

Nu

mb

er

of

ite

rati

on

sPageRank

Sampling Ratio = 0.1

PREDIcT reduces relative error from [104, 168]% to [0, 11]%

Predicting Time

0.01

0.05

0.1 0.15

0.2 0.25

-0.7

-0.4

0.0

0.3

0.6LJ Wiki UK-2002

Sampling Ratio

Rela

tive E

rror

Tim

e

Semi-clustering

0.01 0.05 0.1 0.15 0.2 0.25-0.2

0.0

0.1

0.3

0.5LJ Wiki UK-2002

Sampling Ratio

Rela

tive E

rror

Tim

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Neighborhood estimation

[10, 30]% relative error for 15% sample

Algorithms with variable work/iteration• Cumulated impact of: # of iterations and per iteration

resources

Impact

• PREDIcT: Experimental methodology for estimating key features and runtime for iterative analytics on graphs

• Enables key feature prediction: pluggable transformations, and runtime prediction: cost model

• Accurate empirical solution:• Iterations: [0, 11]% (opposed to [104,168]%)• Time: [10, 30]%

http://dias.epfl.ch/predict

Thank you!

Backup slides

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Cost Model: Model Fitting

Multivariate regression

Pool of BSP features

Model Fitting

Historical runs

• Training data: sample run + historical runs (if such runs exist)

• Customizable cost model (per input algorithm)

F (X1,…,Xk)

Sample run

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Cost Model

compute message sync

Itera

tion

W1 W2W3

Active vertices,Message countsMessage counts,Message sizes,Locality of messagesPartitioning scheme / skew

• Bulk Synchronous Parallel execution model

• Specialized for network intensive algorithms

• Each phase but sync: multivariate regression

• Synchronization modeled implicitly



Customized Cost Model for Bulk Synchronous Parallel Execution Model

Feasibility Analysis

PR (UK) PR (TW) SC (UK) CC (UK) CC (TW)0

1250

2500

3750

5000

Actual runSample run

Runti

me (

sec)

20Feasible for algorithms dominated by iteration time

Context: BSP Processing Model

Giraph BSPW1

W2

W3

W4

Vertex centric model: Each vertex performs local processing, then messaging

Algorithms in BSP are inherently iterative

Itera

tion

W1 W2W3

compute message sync

Bulk Synchronous Parallel (BSP) W4

Prediction

Cost ModelF (X1,…,Xk)

Extrapolator

Runtime

Scaled features

Profiled features

Sample run Estimated actual run

Two extrapolation factors:• on edges• on vertices

Customized cost model for the Bulk Synchronous Parallel execution model: i.e., Giraph BSP