7th biennial ptolemy miniconference berkeley, ca february 13, 2007 scheduling data-intensive...

7th Biennial Ptolemy Miniconference

Berkeley, CAFebruary 13, 2007

Scheduling Data-Intensive Workflows

Tim H. Wong, Daniel Zinn, Bertram Ludäscher

(UC Davis)

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Outline

Problem motivation Assumptions Cost model Problem formalization Different “simplifications” and their complexity Prototypical Java implementation for Kepler Summary

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Motivation: Distributed Execution of Scientific Workflows

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Motivation: Distributed Execution of Scientific Workflows

Process a set of data on a set of machines

GOAL:Minimize WF-Execution time!Allocation Problem: Which actors are computed on which hosts?

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Assumptions

Arbitrary data size Arbitrary machine speed Arbitrary bandwidth Arbitrary number of inputs Scientific workflow is a DAG (!)

GRID COMPUTING

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Cost Model

Communication Time: TC

Function Execution Time: TE

Total Time: TT = TC + TE

Shipping and Handling Problem:Schedule all tasks such that the total time is minimal

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Problem Variants and Complexities

Task Handling Problem (THP) Data Shipping Problem (DSP)

Reduction from Task Scheduling Problem [ERLA94]

Reduction from Multiprocessor Scheduling Problem [KA99]

Reduction from 1-Multiterminal Cut

Shipping and Handling Problem (SHP)Communication Cost: Non-uniformFunction Execution Cost: Non-uniformComplexity: NP-complete

Communication Cost: ZeroFunction Execution Cost: Non-uniformComplexity: NP-complete

Communication Cost: Non-uniformFunction Execution Cost: ZeroComplexity: NP-complete

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easy-DSP: Uniform Transfer Rate, Uniform Data Size

Given: Directed Acyclic Graph,

Set of Colors Some vertices are already

colored Edge Weight = 1, if two adjacent

vertices are of different colorsEdge Weight = 0, otherwise

TASK: Color the rest of the vertices

such that total weight is minimal!

Cost Model:Minimize TotalShipped Volume!

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1 - Multi-Terminal CUT

Given: Undirected Graph: G = (V,E) Set of Terminals: S V Edge Weights: 1

TASK: Find a multi-way cut of G with a

minimum number of edges

NP-Complete for more than 3 Terminals!

Minimize #edgesbetween differentterminals!

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Reduction: 1-MTC <= DSP

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DSP 1-MTC

“Order graph Color terminals”

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Reduction: 1-MTC <= DSP

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1

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1

1

1 11

1

?!

DSP 1-MTC

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Reduction: 1-MTC <= DSP

4 4

1

11

1

1

1 11

1

!

DSP 1-MTC

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NP-Hard, ...But: Need to solve

Greedy Algorithm Dynamic Programing Algorithm

Investigate Approximation Algorithms for MTC/related !

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Prototypical Implementation ...

abstractonly somenodes assigned

concreteall nodes assigned

scheduling

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Prototypical Implementation ... in Kepler!

Abstract Workflow ...

SCHEDULING

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Prototypical Implementation ... in Kepler!

Concrete Workflow ...

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Future Work

Use Heuristics about looping to guess multiplicities(then not ACYCLIC any more!)

Investigate approximation algorithms with error guarantees for 1-MTC => try to apply for DSP

ALSO: Relevant for COMAD Workflows:can be “compiled” into a low-level conventional WF

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Summary

Bad news Scheduling is hard DSP is hard (for BEST plans)

Good news Finding a quite good plan is easy Greedy/Dynamic Algorithms

Open Problems Approximation Quality of “simple algorithms”? When do they perform badly? Does this occur often in real-life workflows?

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References

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Thank You. Questions?