Mapping Heuristics in Heterogeneous...

Mapping Heuristics in Heterogeneous Computing

Multiple Processor Systems (EECC756)

Dr. Shaaban

Alexandru SamachisaDmitriy Bekker

May 18, 2006

Multiple Processor Systems (EECC756) Spring 2006

OverviewIntroduction

Mapping overviewHomogenous computing vs. heterogeneous computing

Task mapping heuristics (for HC)Overview (static, dynamic, online, batch)DAG used in examplesPerformance metrics

Selected algorithmsHEFT, CPOP, MCT, Min-min, Max-min, Sufferage

Conclusion


Mapping OverviewMapping (matching and scheduling) of processesonto processorsGoal

Assign process to best suited machineMaximize performance

NP-completeHeuristics exist to optimize mapping performance

Best heuristic to use depends onStatic or dynamic?Task arrival rateNumber of tasks

P0

Processors

P1

P2 P3

p0 p1

p2 p3

Parallelprogram

Mapping


Homogenous vs. Heterogeneous Computing

Homogenous computingBest for fixed task grain size (most common)Support for single mode of parallelismCustom architecture

Heterogeneous computing (HC)

Variable task grain sizeSupport for multiple modes of parallelismMachines in cluster may be different

Mapping much simpler in homogenous computing

Known task sizeKnown task execution time on any node

In HC…Task size and machine performance variesMapping heuristic must find optimal (or sub-optimal) machine for each task


Mapping HeuristicsStatic Mapping

Performed at compile time (off-line)Expected Time to Compute (ETC) is known for all tasks

Dynamic MappingPerformed at run-timeETC only known for currently mapping tasksTwo modes

On-line (one task mapped at a time)Batch (acquire a number of tasks into meta-task and then map)


DAG used in examples


Performance MetricsExpected execution time (EET)

Assumes no load on systemExpected completion time (ECT)

ECT = begin time + EETMakespan (maximum ECT)Average sharing penalty

Based on waiting time of task Good measure of quality of service

Schedule length ratio (SLR)Makespan normalized to sum of minimum computation costs on minimum critical path (for static mapping)


HEFT and CPOPBoth static algorithms (know whole DAG)Prioritize based on ranks (recursive)

Upward rank

Downward rank


HEFTGoal: schedule task on “best” processor, minimize finish timeGives each task in the graph a priority based on the communication costs and computation (decreasing upward rank)Iterate through the tasks based on priority and assign the process with the earliest finish time for the taskComplexity: O(ep)

e = edgesp = processors

Order n2 complexity for very dense graphs (n is number of tasks)

n1

n5n6

n4

n3

n2

n7

n8n9

n10

10

20

30

40

50

60

70

80

90

0P1 P2 P3


CPOPSimilar to HEFTPrioritizes the tasks based on communication and computation cost (summation of upward and downward ranks)Determines critical path processor (minimized cumulative computation costs of tasks on path)Assign critical path task to critical path processor

If task not in critical path, assign it to processor which minimizes earliest execution finish time

Same complexity as HEFT: O(ep)

n1

n5

n6

n4n3

n2

n7

n8

n9

n10

10

20

30

40

50

60

70

80

90

0P1 P2 P3


On-line modeEach task is assigned as soon as receivedUsually easy to implement since the selection is based on a simple criteriaHeuristics: Minimum completion time, minimum execution time, switching algorithm, K-percent best, etc.The on-line heuristics usually need O(m) time to assign the process


MCT

978889N10

706968N9

715762N8

618039N7

464245N6

373944N5

442645N4

463432N3

274640N2

91614N1

P3P2P1n1

n5n6

n4n3

n2

n7

n8

n9

n10

10

20

30

40

50

60

70

80

90

0P1 P2 P3

Assigns each task on arrival to the process that yields the MCT for that task

Complexity: O(m)


Batch modeThe batch mode heuristics assume that tasks are independentThe set of independent tasks that is being processed is called a Meta-taskAll tasks get remapped at every mapping intervalOur assumptions:

Each level of dependency is constitutes a meta-taskOnce a task is assigned, it will not be remapped at the next mapping event

Meta-task 1

Meta-task 2

Meta-task 3

Meta-task 4


Min-min (meta-task 2)

183936N6

193332N5

262631N4

283432N3

274640N2

P3P2P1n1

n6

n5n4

n3

n2

n7

n8

n9

n10

10

20

30

40

50

60

70

80

90

0P1 P2 P3

283332N5

352631N4

373432N3

364640N2

P3P2P1

283932N5

373432N3

364640N2

P3P2P1

473432N3

464640N2

P3P2P1

464645N2

P3P2P1

Complexity: O(S2m) per meta-task, where m is the number of machines and S is the number of tasks in the meta-task


Max-min (meta-task 2)

373936N6

383332N5

452631N4

464640N2

P3P2P1

n1

n5

n6

n4

n3

n2

n7

n8

n9

n10

10

20

30

40

50

60

70

80

90

0P1 P2 P3

183936N6

193332N5

262631N4

283432N3

274640N2

P3P2P1

373953N6

383352N5

452653N4

P3P2P1

473352N5

542653N4

P3P2P1

544153N4

P3P2P1



Sufferage (meta-task 2)n1

n5

n6

n4

n3

n2

n7

n8

n9

n10

10

20

30

40

50

60

70

80

90

0P1 P2 P3

18183936N6

13193332N5

0262631N4

4283432N3

13274640N2

SP3P2P1

4283332N5

5352631N4

2373432N3

4364640N2

SP3P2P1

4283932N5

7373932N3

4364640N2

SP3P2P1

11283944N5

9364645N2

SP3P2P1

1464645N2

SP3P2P1



ConclusionThe static mapping heuristics tend to be dropped in favor of the dynamic ones due to their advantagesThe on-line heuristics are the easiest ones to implement and usually have good results when compared to other dynamic mapping heuristicsThe batch heuristics are harder to implement, and they also can present the problem of task starvation – need to add an aging mechanism to solve this issueWhich dynamic heuristics to use when?

On-line when task arrival rate is low (tasks mapped immediately)Batch when task arrival rate is high (group tasks into meta-tasks, then map them)


Conclusion cont’dThe performance results for the example shown here does not reflect the actual performances of the presented heuristicsHowever, the selected heuristics are among the best performing ones in their categoriesMapping on heterogeneous systems is a lot more complex (if done correctly) than on homogenous systems


ReferencesT. D. Braun, H. J. Siegel, N. Beck, L. Boloni, M. Maheswaran, A. I. Reuther, J. P. Robertson, M. D. Theys, B. Yao, R. F. Freund, and D. Hensgen, “A Comparison Study of Static Mapping Heuristics for a Class of Metatasks on Heterogeneous Computing Systems,” 8th IEEE Heterogeneous Computing Workshop (HCW’99), Apr. 1999.M. Maheswaran, A. Shoukat, H. J. Siegel, D. Hensgen, and R. F. Freund, “Dynamic Matching and Scheduling of a Class of Independent Tasks onto Heterogeneous Computing Systems,” 8th IEEE Heterogeneous Computing Workshop (HCW’99), Apr. 1999.M. Shaaban, EECC756 Lecture Slides, Spring 2006.H. Topcuoglu, S. Hariri, M. Wu, “Performance-effective and Low-complexity Task Scheduling for Heterogeneous Computing,” IEEE Transaction on Parallel and Distributed Systems, vol. 13, no. 3, pp. 260 – 274, March 2002.

Mapping Heuristics in Heterogeneous...

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