Static scheduling of conditional branches in parallel programs

68 Pages·2.7 MB·en_US

by  George, Robert Tyler.

NAVAL POSTGRADUATE SCHOOL
MONTEREY, CALIFORNU
THh:SIS
STATIC SCHEDULING OF CONDITIONAL
BRANCHES IN PARALLEL PROGRAMS
by
Robert T. George
December 1996
Thesis Advisor: Theodore Lewis
Approved for public release; distribution is unlimited
Thesis
G2633

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E)ecember 3-996 Master's Thesis
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Static Scheduling ofConditional Branches in Parallel Programs(U)
6.AUTHOR(S)
George, Robert Tyler
7.PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES) 8.PERFORMINGORGANIZATION
Naval Postgraduate School REPORTNUMBER
Monterey, CA 93943-5000
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Army Research Laboratory AGENCYREPORTNUMBER
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11.SUPPLEMENTARYNOTES
The views expressed in this thesis are those ofthe author and do not reflect the official policy or position
ofthe Department ofDefense or the United States Government.
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13.ABSTRACT(Maximum200words)
The problem ofscheduling parallel program tasks on multiprocessor systems is known to be NP-complete in
its general form. When non-determinism is added to the scheduling problem through loops and conditional
branching, an optimal solution is even harder to obtain. The intractability ofobtaining an optimal solution for the
general scheduhng problemhas led to the introduction ofa large numberofscheduling heuristics. These heuristics
consider many real-world factors, such as communication overhead, target machine topology, and the trade-off
between exploiting the parallelism in aparallel program and the resulting scheduling overhead.
Wepresenttheprobabilisticmergeheuristic-- in which aunified schedule ofall possibleexecution instances
is generated by successively scheduling tasks in order oftheir execution probabilities. When a conditional task is
scheduled, we first attempt to merge the task with the time slot ofapreviously scheduled task which is a member
ofadifferentexecution instance.
We have foundthat the merge scheduler produces schedules which are 10% fasterthan previous techniques.
More importantly, however, we show that the probabilistic merge heuristic is significantly more scalable — being
able to schedule branch and precedence graphs which exceed 50 nodes.
14.SUBJECTTERMS 15.NUMBEROFPAGES
Parallel Processing, Scheduling 64
16.PRICECODE
17.SECURfTYCLASSIFICATION 18.SECURITYCLASSIFICATION 19.SECURITYCLASSIFICATION 20.LIMfTATIONOFABSTRACT
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Approved for public release; distribution is unlimited
STATIC SCHEDULING OF CONDITIONAL
BRANCHES IN PARALLEL PROGRAMS
Robert Tyler George
Army Research Laboratory
B.S., Virginia Polytechnic and State University, 1988
Submitted in partial fulfillmeht ofthe
requirements for the degree of
MASTER OF SCIENCE IN COMPUTER SCIENCE
from the
NAVAL POSTGRADUATE SCHOOL
December 1996

DUDLEY KNOX LIBRARY
NAVAL POSTGRADUATE SCHOOl
A locnpT^ A r-r^ MONTEREY CA 93943-5101
The problem of scheduling parallel program tasks on multiprocessor systems is
known to be NP-compIete in its general form. When non-determinism is added to the
scheduling problem through loops and conditional branching, an optimal solution is even
harder to obtain. The intractability of obtaining an optimal solution for the general
scheduling problem has led to the introduction ofa large number of scheduling heuristics.
These heuristicsconsidermany real-world factors, such as communication overhead, target
machine topology, and the trade-off between exploiting the parallelism in a parallel
program and the resulting scheduling overhead.
We present the probabilistic merge heuristic ~ in which a unified schedule of all
possible execution instances is generated by successively scheduling tasks in order oftheir
execution probabilities. When aconditional taskis scheduled, we first attempt to merge the
task with the time slot of a previously scheduled task which is a member of a different
execution instance.
We have found that the merge scheduler produces schedules which are 10% faster
than previous techniques. More importantly, however, we show that the probabilistic
merge heuristic is significantly more scalable — being able to schedule branch and
precedence graphs which exceed 50 nodes.
VI
TABLE OF CONTENTS
INTRODUCTION
I. 1
BACKGROUND
A.
1
B. SCHEDULING PARALLEL TASKS 2
THE SCHEDULING PROBLEM
C. 3
THE TASK SCHEDULING MODEL
n. 5
BACKGROUND
A. 5
TARGET MACHINE
B. 5
PARALLEL PROGRAM TASKS
C. 6
L Modeling Conditional Branching 7
2. Execution and Communication Cost 8
THE SCHEDULE
D. 10
E. PERFORMANCE CRITERIA 10
m. LIST SCHEDULING 13
BACKGROUND
A. 13
B. LIST SCHEDULING 13
C COMMUNICATION ISSUES
15
1. Parallelism Versus Communication Delay 15
2. Level Alteration 16
3. List Scheduling with Communication 17
4. Program and Machine Models 18
5. Terminology 19
6. General List-Scheduling Heuristic 20
D. THE MAPPING HEURISTIC (MH) 21
I. Routing Tables 24
IV. SCHEDULING NON-DETERMINISTIC TASK GRAPHS 27
BACKGROUND
A. 27
B. REDUCING THE DEGREE OF NON-DETERMINISM 27
1. Similarity in Non-deterministic Task Graphs 28
2. The Reduced Task Graph 29
C. THE MULTI-PHASE APPROACH 32
1. Phase 1: Generate 33
2. Phase 2: Construct 35
3. Phase 3: Schedule 36
4. Phase 4: Merge 38
V. THE PROBABILISTIC MERGE HEURISTIC 43
A. DESIGN CONSIDERATIONS 43
B. THE PROBABILISTIC MERGE HEURISTIC 45
1. Level Calculation 45
2. Probabilistic Merging 45
C
SIMULATION RESULTS 49
1. Scheduling Efficiency 49
vu
2. Schedule Runtimes 50
CONCLUSIONS
D. 51
LIST OF REFERENCES 53
INITL\L DISTRIBUTION LIST 55
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