816 research outputs found
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
Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling
This paper establishes performance guarantees for online algorithms that
schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the
expected total weighted completion time. Prior work on unrelated machine
scheduling with stochastic jobs was restricted to the offline case, and
required linear or convex programming relaxations for the assignment of jobs to
machines. The algorithms introduced in this paper are purely combinatorial. The
performance bounds are of the same order of magnitude as those of earlier work,
and depend linearly on an upper bound on the squared coefficient of variation
of the jobs' processing times. Specifically for deterministic processing times,
without and with release times, the competitive ratios are 4 and 7.216,
respectively. As to the technical contribution, the paper shows how dual
fitting techniques can be used for stochastic and nonpreemptive scheduling
problems.Comment: Preliminary version appeared in IPCO 201
ILP-based approaches to partitioning recurrent workloads upon heterogeneous multiprocessors
The problem of partitioning systems of independent constrained-deadline sporadic tasks upon heterogeneous multiprocessor platforms is considered. Several different integer linear program (ILP) formulations of this problem, offering different tradeoffs between effectiveness (as quantified by speedup bound) and running time efficiency, are presented
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
Scheduling MapReduce Jobs under Multi-Round Precedences
We consider non-preemptive scheduling of MapReduce jobs with multiple tasks
in the practical scenario where each job requires several map-reduce rounds. We
seek to minimize the average weighted completion time and consider scheduling
on identical and unrelated parallel processors. For identical processors, we
present LP-based O(1)-approximation algorithms. For unrelated processors, the
approximation ratio naturally depends on the maximum number of rounds of any
job. Since the number of rounds per job in typical MapReduce algorithms is a
small constant, our scheduling algorithms achieve a small approximation ratio
in practice. For the single-round case, we substantially improve on previously
best known approximation guarantees for both identical and unrelated
processors. Moreover, we conduct an experimental analysis and compare the
performance of our algorithms against a fast heuristic and a lower bound on the
optimal solution, thus demonstrating their promising practical performance
Scheduling Algorithms for Procrastinators
This paper presents scheduling algorithms for procrastinators, where the
speed that a procrastinator executes a job increases as the due date
approaches. We give optimal off-line scheduling policies for linearly
increasing speed functions. We then explain the computational/numerical issues
involved in implementing this policy. We next explore the online setting,
showing that there exist adversaries that force any online scheduling policy to
miss due dates. This impossibility result motivates the problem of minimizing
the maximum interval stretch of any job; the interval stretch of a job is the
job's flow time divided by the job's due date minus release time. We show that
several common scheduling strategies, including the "hit-the-highest-nail"
strategy beloved by procrastinators, have arbitrarily large maximum interval
stretch. Then we give the "thrashing" scheduling policy and show that it is a
\Theta(1) approximation algorithm for the maximum interval stretch.Comment: 12 pages, 3 figure
Optimal Algorithms for Scheduling under Time-of-Use Tariffs
We consider a natural generalization of classical scheduling problems in
which using a time unit for processing a job causes some time-dependent cost
which must be paid in addition to the standard scheduling cost. We study the
scheduling objectives of minimizing the makespan and the sum of (weighted)
completion times. It is not difficult to derive a polynomial-time algorithm for
preemptive scheduling to minimize the makespan on unrelated machines. The
problem of minimizing the total (weighted) completion time is considerably
harder, even on a single machine. We present a polynomial-time algorithm that
computes for any given sequence of jobs an optimal schedule, i.e., the optimal
set of time-slots to be used for scheduling jobs according to the given
sequence. This result is based on dynamic programming using a subtle analysis
of the structure of optimal solutions and a potential function argument. With
this algorithm, we solve the unweighted problem optimally in polynomial time.
For the more general problem, in which jobs may have individual weights, we
develop a polynomial-time approximation scheme (PTAS) based on a dual
scheduling approach introduced for scheduling on a machine of varying speed. As
the weighted problem is strongly NP-hard, our PTAS is the best possible
approximation we can hope for.Comment: 17 pages; A preliminary version of this paper with a subset of
results appeared in the Proceedings of MFCS 201
Non-clairvoyant Scheduling Games
In a scheduling game, each player owns a job and chooses a machine to execute
it. While the social cost is the maximal load over all machines (makespan), the
cost (disutility) of each player is the completion time of its own job. In the
game, players may follow selfish strategies to optimize their cost and
therefore their behaviors do not necessarily lead the game to an equilibrium.
Even in the case there is an equilibrium, its makespan might be much larger
than the social optimum, and this inefficiency is measured by the price of
anarchy -- the worst ratio between the makespan of an equilibrium and the
optimum. Coordination mechanisms aim to reduce the price of anarchy by
designing scheduling policies that specify how jobs assigned to a same machine
are to be scheduled. Typically these policies define the schedule according to
the processing times as announced by the jobs. One could wonder if there are
policies that do not require this knowledge, and still provide a good price of
anarchy. This would make the processing times be private information and avoid
the problem of truthfulness. In this paper we study these so-called
non-clairvoyant policies. In particular, we study the RANDOM policy that
schedules the jobs in a random order without preemption, and the EQUI policy
that schedules the jobs in parallel using time-multiplexing, assigning each job
an equal fraction of CPU time
New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria
In this paper, we are interested in parallel identical machine scheduling
problems with preemption and release dates in case of a regular criterion to be
minimized. We show that solutions having a permutation flow shop structure are
dominant if there exists an optimal solution with completion times scheduled in
the same order as the release dates, or if there is no release date. We also
prove that, for a subclass of these problems, the completion times of all jobs
can be ordered in an optimal solution. Using these two results, we provide new
results on polynomially solvable problems and hence refine the boundary between
P and NP for these problems
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