969 research outputs found
Throughput Maximization in Multiprocessor Speed-Scaling
We are given a set of jobs that have to be executed on a set of
speed-scalable machines that can vary their speeds dynamically using the energy
model introduced in [Yao et al., FOCS'95]. Every job is characterized by
its release date , its deadline , its processing volume if
is executed on machine and its weight . We are also given a budget
of energy and our objective is to maximize the weighted throughput, i.e.
the total weight of jobs that are completed between their respective release
dates and deadlines. We propose a polynomial-time approximation algorithm where
the preemption of the jobs is allowed but not their migration. Our algorithm
uses a primal-dual approach on a linearized version of a convex program with
linear constraints. Furthermore, we present two optimal algorithms for the
non-preemptive case where the number of machines is bounded by a fixed
constant. More specifically, we consider: {\em (a)} the case of identical
processing volumes, i.e. for every and , for which we
present a polynomial-time algorithm for the unweighted version, which becomes a
pseudopolynomial-time algorithm for the weighted throughput version, and {\em
(b)} the case of agreeable instances, i.e. for which if and only
if , for which we present a pseudopolynomial-time algorithm. Both
algorithms are based on a discretization of the problem and the use of dynamic
programming
Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach
We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective
is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem.
We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can
be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper
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
Preemptive scheduling on uniform parallel machines with controllable job processing times
In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan
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