5 research outputs found
An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines
We study the scheduling problem on unrelated machines in the mechanism design
setting. This problem was proposed and studied in the seminal paper (Nisan and
Ronen 1999), where they gave a 1.75-approximation randomized truthful mechanism
for the case of two machines. We improve this result by a 1.6737-approximation
randomized truthful mechanism. We also generalize our result to a
-approximation mechanism for task scheduling with machines, which
improve the previous best upper bound of $0.875m(Mu'alem and Schapira 2007)
Average-case Approximation Ratio of Scheduling without Payments
Apart from the principles and methodologies inherited from Economics and Game
Theory, the studies in Algorithmic Mechanism Design typically employ the
worst-case analysis and approximation schemes of Theoretical Computer Science.
For instance, the approximation ratio, which is the canonical measure of
evaluating how well an incentive-compatible mechanism approximately optimizes
the objective, is defined in the worst-case sense. It compares the performance
of the optimal mechanism against the performance of a truthful mechanism, for
all possible inputs.
In this paper, we take the average-case analysis approach, and tackle one of
the primary motivating problems in Algorithmic Mechanism Design -- the
scheduling problem [Nisan and Ronen 1999]. One version of this problem which
includes a verification component is studied by [Koutsoupias 2014]. It was
shown that the problem has a tight approximation ratio bound of (n+1)/2 for the
single-task setting, where n is the number of machines. We show, however, when
the costs of the machines to executing the task follow any independent and
identical distribution, the average-case approximation ratio of the mechanism
given in [Koutsoupias 2014] is upper bounded by a constant. This positive
result asymptotically separates the average-case ratio from the worst-case
ratio, and indicates that the optimal mechanism for the problem actually works
well on average, although in the worst-case the expected cost of the mechanism
is Theta(n) times that of the optimal cost
A New Lower Bound for Deterministic Truthful Scheduling
We study the problem of truthfully scheduling tasks to selfish
unrelated machines, under the objective of makespan minimization, as was
introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the
current gap of on the approximation ratio of deterministic truthful
mechanisms is a notorious open problem in the field of algorithmic mechanism
design. We provide the first such improvement in more than a decade, since the
lower bounds of (for ) and (for ) by
Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07],
respectively. More specifically, we show that the currently best lower bound of
can be achieved even for just machines; for we already get
the first improvement, namely ; and allowing the number of machines to
grow arbitrarily large we can get a lower bound of .Comment: 15 page
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