5,923 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
Minimizing Flow-Time on Unrelated Machines
We consider some flow-time minimization problems in the unrelated machines
setting. In this setting, there is a set of machines and a set of jobs,
and each job has a machine dependent processing time of on machine
. The flow-time of a job is the total time the job spends in the system
(completion time minus its arrival time), and is one of the most natural
quality of service measure. We show the following two results: an
approximation algorithm for minimizing the
total-flow time, and an approximation for minimizing the maximum
flow-time. Here is the ratio of maximum to minimum job size. These are the
first known poly-logarithmic guarantees for both the problems.Comment: The new version fixes some typos in the previous version. The paper
is accepted for publication in STOC 201
- β¦