Received: 2 May 2016 Revised: 17 August 2016 Accepted: 23 September 2016
DOI 10.1002/cpe.4024
SPECIAL ISSUE PAPER
Schedule length minimization of parallel applications with
energy consumption constraints using heuristics on
heterogeneous distributed systems
Guoqi Xie
1,2
Xiongren Xiao
1,2
Renfa Li
1,2
Keqin Li
1,3
1
College of Computer Science and Electronic
Engineering, Hunan University, Changsha,
China
2
Key Laboratory for Embedded and Network
Computing of Hunan Province, Changsha,
China
3
Department of Computer Science, State
University of New York, Albany, NY, USA
Correspondence
Guoqi Xie, College of Computer Science and
Electronic Engineering, Hunan University,
Changsha, Hunan 410082, China.
Email: xgqman@hnu.edu.cn
Funding Information
National Key Research and Development Plan
of China, Grant/Award Number:
2012AA01A301-01 and 2016YFB0200405;
National Natural Science Foundation of China,
Grant/Award Number: 61432005, 61173036,
61300037, 61370095, 61300039, 61502162,
61379115, 61502405, 61402170 and
61370097; China Postdoctoral Science
Foundation, Grant/Award Number:
2016M592422
Summary
Energy consumption is one of the primary design constraints in heterogeneous parallel and dis-
tributed systems ranging from small embedded devices to large-scale data centers. The problem
of minimizing the schedule length of an energy consumption-constrained parallel application has
been studied recently in homogeneous systems with a shared memory. Toadopttheheterogeneity
and distribution of high-performance computing systems, this study solves the problem of mini-
mizing the schedule length of an energy consumption-constrained parallel application in hetero-
geneous distributed systems based on a dynamic voltage and frequency scaling energy-efficient
design technique. Theaforementionedproblemisdivided into 2 subproblems in this study, namely,
satisfying energy consumption constraint and minimizing schedule length. The first subproblem
is solved by transferring the energy consumption constraint of the application to that of each
task, whereas the second subproblem is solved by heuristically scheduling each task with low time
complexity.Experiments using both fast Fourier transformand Gaussian elimination parallel appli-
cations show that the actual energy consumption values do not always exceed but a re close to the
given energy consumption constraints. In addition, the minimum schedule lengths are generated
using the proposed algorithm.
KEYWORDS
energy consumption, heterogeneous systems, parallel applications, schedule length
1 INTRODUCTION
1.1 Background
Recent trends in the microprocessor industry have important impli-
cations for the design of high-performance computing systems.
Performance is improved while keeping energy consumption to a mini-
mum by increasing the number of heterogeneous processors and cores.
This trend has reached the deployment stage in heterogeneous paral-
lel and distributed systems, which range from small embedded devices
to large-scale data centers. A number of heterogeneous processors
and cores in these systems are expected to increase dramatically in
the near future. For these systems, energy consumption is one of the
primary design constraints. The popular energy consumption optimiza-
tion technique, namely, dynamic voltage and frequency scaling (DVFS),
achieves energy-efficient optimization by simultaneously scaling
down the supply voltage and frequency of a processor while tasks are
running to explore the trade-off between energy consumption and
execution time.
1–3
A parallel application with precedence-constrained tasks at a high
level of heterogeneous distributed systems is described by a directed
acyclic graph (DAG),
4–6
where nodes represent tasks and edges repre-
sent communication messages between tasks. Reducing the scheduling
length (also called makespan) for fastest execution of a DAG-based
parallel application is the main concern in system performance.
4,7–9
The schedule length is represented as the time span that from the
start time instant of first task to the finish time instant of the last
task. Scheduling tasks on heterogeneous processors with the objective
of minimizing the schedule length of a DAG-based parallel applica-
tion is a well-known nondeterministic polynomial–hard optimization
problem, and numerous heuristic list scheduling algorithms have been
proposed to generate near-optimal solutions of the problem.
4–6
Sim-
ilarly, minimizing schedule length of a DAG-based parallel application
Concurrency Computat: Pract Exper 2016; 1–10 wileyonlinelibrary.com/journal/cpe Copyright © 2016 John Wiley & Sons, Ltd. 1