1,359 research outputs found
Online Makespan Minimization with Parallel Schedules
In online makespan minimization a sequence of jobs
has to be scheduled on identical parallel machines so as to minimize the
maximum completion time of any job. We investigate the problem with an
essentially new model of resource augmentation. Here, an online algorithm is
allowed to build several schedules in parallel while processing . At
the end of the scheduling process the best schedule is selected. This model can
be viewed as providing an online algorithm with extra space, which is invested
to maintain multiple solutions. The setting is of particular interest in
parallel processing environments where each processor can maintain a single or
a small set of solutions.
We develop a (4/3+\eps)-competitive algorithm, for any 0<\eps\leq 1, that
uses a number of 1/\eps^{O(\log (1/\eps))} schedules. We also give a
(1+\eps)-competitive algorithm, for any 0<\eps\leq 1, that builds a
polynomial number of (m/\eps)^{O(\log (1/\eps) / \eps)} schedules. This value
depends on but is independent of the input . The performance
guarantees are nearly best possible. We show that any algorithm that achieves a
competitiveness smaller than 4/3 must construct schedules. Our
algorithms make use of novel guessing schemes that (1) predict the optimum
makespan of a job sequence to within a factor of 1+\eps and (2)
guess the job processing times and their frequencies in . In (2) we
have to sparsify the universe of all guesses so as to reduce the number of
schedules to a constant.
The competitive ratios achieved using parallel schedules are considerably
smaller than those in the standard problem without resource augmentation
Energy-Efficient Multiprocessor Scheduling for Flow Time and Makespan
We consider energy-efficient scheduling on multiprocessors, where the speed
of each processor can be individually scaled, and a processor consumes power
when running at speed , for . A scheduling algorithm
needs to decide at any time both processor allocations and processor speeds for
a set of parallel jobs with time-varying parallelism. The objective is to
minimize the sum of the total energy consumption and certain performance
metric, which in this paper includes total flow time and makespan. For both
objectives, we present instantaneous parallelism clairvoyant (IP-clairvoyant)
algorithms that are aware of the instantaneous parallelism of the jobs at any
time but not their future characteristics, such as remaining parallelism and
work. For total flow time plus energy, we present an -competitive
algorithm, which significantly improves upon the best known non-clairvoyant
algorithm and is the first constant competitive result on multiprocessor speed
scaling for parallel jobs. In the case of makespan plus energy, which is
considered for the first time in the literature, we present an
-competitive algorithm, where is the total number of
processors. We show that this algorithm is asymptotically optimal by providing
a matching lower bound. In addition, we also study non-clairvoyant scheduling
for total flow time plus energy, and present an algorithm that achieves -competitive for jobs with arbitrary release time and
-competitive for jobs with identical release time. Finally,
we prove an lower bound on the competitive ratio of
any non-clairvoyant algorithm, matching the upper bound of our algorithm for
jobs with identical release time
Energy Efficient Scheduling via Partial Shutdown
Motivated by issues of saving energy in data centers we define a collection
of new problems referred to as "machine activation" problems. The central
framework we introduce considers a collection of machines (unrelated or
related) with each machine having an {\em activation cost} of . There
is also a collection of jobs that need to be performed, and is
the processing time of job on machine . We assume that there is an
activation cost budget of -- we would like to {\em select} a subset of
the machines to activate with total cost and {\em find} a schedule
for the jobs on the machines in minimizing the makespan (or any other
metric).
For the general unrelated machine activation problem, our main results are
that if there is a schedule with makespan and activation cost then we
can obtain a schedule with makespan \makespanconstant T and activation cost
\costconstant A, for any . We also consider assignment costs for
jobs as in the generalized assignment problem, and using our framework, provide
algorithms that minimize the machine activation and the assignment cost
simultaneously. In addition, we present a greedy algorithm which only works for
the basic version and yields a makespan of and an activation cost .
For the uniformly related parallel machine scheduling problem, we develop a
polynomial time approximation scheme that outputs a schedule with the property
that the activation cost of the subset of machines is at most and the
makespan is at most for any
Some recent results in the analysis of greedy algorithms for assignment problems
We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems
Scheduling Bidirectional Traffic on a Path
We study the fundamental problem of scheduling bidirectional traffic along a
path composed of multiple segments. The main feature of the problem is that
jobs traveling in the same direction can be scheduled in quick succession on a
segment, while jobs in opposing directions cannot cross a segment at the same
time. We show that this tradeoff makes the problem significantly harder than
the related flow shop problem, by proving that it is NP-hard even for identical
jobs. We complement this result with a PTAS for a single segment and
non-identical jobs. If we allow some pairs of jobs traveling in different
directions to cross a segment concurrently, the problem becomes APX-hard even
on a single segment and with identical jobs. We give polynomial algorithms for
the setting with restricted compatibilities between jobs on a single and any
constant number of segments, respectively
Games and Mechanism Design in Machine Scheduling – An Introduction
In this paper, we survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents need to interact in order to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically in order to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical Optimization, Game Theory, and Economic Theory. The paper therefore briefly introduces the most important of the underlying concepts, and gives a selection of typical research questions and recent results, focussing on applications to machine scheduling problems. This includes the study of the so-called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.computer science applications;
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