704 research outputs found
Maximizing the Minimum Load for Selfisch Agents
We consider the problem of maximizing the minimum load for
machines that are controlled by selfish agents, who are only
interested in maximizing their own profit. Unlike the classical
load balancing problem, this problem
has not been considered for selfish agents until now.
For a constant number of machines, , we show a
monotone polynomial time approximation scheme (PTAS) with running
time that is linear in the number of jobs. It uses a new
technique for reducing the number of jobs while remaining close
to the optimal solution. We also present an FPTAS for the classical
machine covering problem, i.e., where no selfish agents are involved
(the previous best result for this case was a PTAS)
and use this to give a monotone FPTAS.
Additionally, we give a monotone approximation algorithm with
approximation ratio where can
be chosen arbitrarily small and is the (real) speed of
machine . Finally we give improved results for two machines
A unified approach to truthful scheduling on related machines
We present a unified framework for designing deterministic monotone
polynomial time approximation schemes (PTAS's) for a wide class of scheduling
problems on uniformly related machines. This class includes (among others)
minimizing the makespan, maximizing the minimum load, and minimizing the l_p
norm of the machine loads vector. Previously, this kind of result was only
known for the makespan objective. Monotone algorithms have the property that an
increase in the speed of a machine cannot decrease the amount of work assigned
to it. The key idea of our novel method is to show that for goal functions that
are sufficiently well-behaved functions of the machine loads, it is possible to
compute in polynomial time a highly structured nearly optimal schedule.
Monotone approximation schemes have an important role in the emerging area of
algorithmic mechanism design. In the game-theoretical setting of these
scheduling problems there is a social goal, which is one of the objective
functions that we study. Each machine is controlled by a selfish
single-parameter agent, where its private information is its cost of processing
a unit sized job, which is also the inverse of the speed of its machine. Each
agent wishes to maximize its own profit, defined as the payment it receives
from the mechanism minus its cost for processing all jobs assigned to it, and
places a bid which corresponds to its private information. For each one of the
problems, we show that we can calculate payments that guarantee truthfulness in
an efficient manner. Thus, there exists a dominant strategy where agents report
their true speeds, and we show the existence of a truthful mechanism which can
be implemented in polynomial time, where the social goal is approximated within
a factor of 1+epsilon for every epsilon>0
Prior-Independent Mechanisms for Scheduling
We study the makespan minimization problem with unrelated selfish machines
under the assumption that job sizes are stochastic. We design simple truthful
mechanisms that under various distributional assumptions provide constant and
sublogarithmic approximations to expected makespan. Our mechanisms are
prior-independent in that they do not rely on knowledge of the job size
distributions. Prior-independent approximation mechanisms have been previously
studied for the objective of revenue maximization [Dhangwatnotai, Roughgarden
and Yan'10, Devanur, Hartline, Karlin and Nguyen'11, Roughgarden, Talgam-Cohen
and Yan'12]. In contrast to our results, in prior-free settings no truthful
anonymous deterministic mechanism for the makespan objective can provide a
sublinear approximation [Ashlagi, Dobzinski and Lavi'09].Comment: This paper will appear in Proceedings of the ACM Symposium on Theory
of Computing 2013 (STOC'13
Makespan Minimization via Posted Prices
We consider job scheduling settings, with multiple machines, where jobs
arrive online and choose a machine selfishly so as to minimize their cost. Our
objective is the classic makespan minimization objective, which corresponds to
the completion time of the last job to complete. The incentives of the selfish
jobs may lead to poor performance. To reconcile the differing objectives, we
introduce posted machine prices. The selfish job seeks to minimize the sum of
its completion time on the machine and the posted price for the machine. Prices
may be static (i.e., set once and for all before any arrival) or dynamic (i.e.,
change over time), but they are determined only by the past, assuming nothing
about upcoming events. Obviously, such schemes are inherently truthful.
We consider the competitive ratio: the ratio between the makespan achievable
by the pricing scheme and that of the optimal algorithm. We give tight bounds
on the competitive ratio for both dynamic and static pricing schemes for
identical, restricted, related, and unrelated machine settings. Our main result
is a dynamic pricing scheme for related machines that gives a constant
competitive ratio, essentially matching the competitive ratio of online
algorithms for this setting. In contrast, dynamic pricing gives poor
performance for unrelated machines. This lower bound also exhibits a gap
between what can be achieved by pricing versus what can be achieved by online
algorithms
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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