4,891 research outputs found
Speed-scaling with no Preemptions
We revisit the non-preemptive speed-scaling problem, in which a set of jobs
have to be executed on a single or a set of parallel speed-scalable
processor(s) between their release dates and deadlines so that the energy
consumption to be minimized. We adopt the speed-scaling mechanism first
introduced in [Yao et al., FOCS 1995] according to which the power dissipated
is a convex function of the processor's speed. Intuitively, the higher is the
speed of a processor, the higher is the energy consumption. For the
single-processor case, we improve the best known approximation algorithm by
providing a -approximation algorithm,
where is a generalization of the Bell number. For the
multiprocessor case, we present an approximation algorithm of ratio
improving the best known result by a factor of
. Notice that our
result holds for the fully heterogeneous environment while the previous known
result holds only in the more restricted case of parallel processors with
identical power functions
Energy-efficient algorithms for non-preemptive speed-scaling
We improve complexity bounds for energy-efficient speed scheduling problems
for both the single processor and multi-processor cases. Energy conservation
has become a major concern, so revisiting traditional scheduling problems to
take into account the energy consumption has been part of the agenda of the
scheduling community for the past few years.
We consider the energy minimizing speed scaling problem introduced by Yao et
al. where we wish to schedule a set of jobs, each with a release date, deadline
and work volume, on a set of identical processors. The processors may change
speed as a function of time and the energy they consume is the th power
of its speed. The objective is then to find a feasible schedule which minimizes
the total energy used.
We show that in the setting with an arbitrary number of processors where all
work volumes are equal, there is a approximation algorithm, where
is the generalized Bell number. This is the first constant
factor algorithm for this problem. This algorithm extends to general unequal
processor-dependent work volumes, up to losing a factor of
in the approximation, where is the maximum
ratio between two work volumes. We then show this latter problem is APX-hard,
even in the special case when all release dates and deadlines are equal and
is 4.
In the single processor case, we introduce a new linear programming
formulation of speed scaling and prove that its integrality gap is at most
. As a corollary, we obtain a
approximation algorithm where there is a single processor, improving on the
previous best bound of
when
Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling
We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed
Survey on Combinatorial Register Allocation and Instruction Scheduling
Register allocation (mapping variables to processor registers or memory) and
instruction scheduling (reordering instructions to increase instruction-level
parallelism) are essential tasks for generating efficient assembly code in a
compiler. In the last three decades, combinatorial optimization has emerged as
an alternative to traditional, heuristic algorithms for these two tasks.
Combinatorial optimization approaches can deliver optimal solutions according
to a model, can precisely capture trade-offs between conflicting decisions, and
are more flexible at the expense of increased compilation time.
This paper provides an exhaustive literature review and a classification of
combinatorial optimization approaches to register allocation and instruction
scheduling, with a focus on the techniques that are most applied in this
context: integer programming, constraint programming, partitioned Boolean
quadratic programming, and enumeration. Researchers in compilers and
combinatorial optimization can benefit from identifying developments, trends,
and challenges in the area; compiler practitioners may discern opportunities
and grasp the potential benefit of applying combinatorial optimization
Energy Efficient Scheduling and Routing via Randomized Rounding
We propose a unifying framework based on configuration linear programs and
randomized rounding, for different energy optimization problems in the dynamic
speed-scaling setting. We apply our framework to various scheduling and routing
problems in heterogeneous computing and networking environments. We first
consider the energy minimization problem of scheduling a set of jobs on a set
of parallel speed scalable processors in a fully heterogeneous setting. For
both the preemptive-non-migratory and the preemptive-migratory variants, our
approach allows us to obtain solutions of almost the same quality as for the
homogeneous environment. By exploiting the result for the
preemptive-non-migratory variant, we are able to improve the best known
approximation ratio for the single processor non-preemptive problem.
Furthermore, we show that our approach allows to obtain a constant-factor
approximation algorithm for the power-aware preemptive job shop scheduling
problem. Finally, we consider the min-power routing problem where we are given
a network modeled by an undirected graph and a set of uniform demands that have
to be routed on integral routes from their sources to their destinations so
that the energy consumption is minimized. We improve the best known
approximation ratio for this problem.Comment: 27 page
Metascheduling of HPC Jobs in Day-Ahead Electricity Markets
High performance grid computing is a key enabler of large scale collaborative
computational science. With the promise of exascale computing, high performance
grid systems are expected to incur electricity bills that grow super-linearly
over time. In order to achieve cost effectiveness in these systems, it is
essential for the scheduling algorithms to exploit electricity price
variations, both in space and time, that are prevalent in the dynamic
electricity price markets. In this paper, we present a metascheduling algorithm
to optimize the placement of jobs in a compute grid which consumes electricity
from the day-ahead wholesale market. We formulate the scheduling problem as a
Minimum Cost Maximum Flow problem and leverage queue waiting time and
electricity price predictions to accurately estimate the cost of job execution
at a system. Using trace based simulation with real and synthetic workload
traces, and real electricity price data sets, we demonstrate our approach on
two currently operational grids, XSEDE and NorduGrid. Our experimental setup
collectively constitute more than 433K processors spread across 58 compute
systems in 17 geographically distributed locations. Experiments show that our
approach simultaneously optimizes the total electricity cost and the average
response time of the grid, without being unfair to users of the local batch
systems.Comment: Appears in IEEE Transactions on Parallel and Distributed System
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