52 research outputs found
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
Exact Distance Oracles for Planar Graphs with Failing Vertices
We consider exact distance oracles for directed weighted planar graphs in the
presence of failing vertices. Given a source vertex , a target vertex
and a set of failed vertices, such an oracle returns the length of a
shortest -to- path that avoids all vertices in . We propose oracles
that can handle any number of failures. More specifically, for a directed
weighted planar graph with vertices, any constant , and for any , we propose an oracle of size
that answers queries in
time. In particular, we show an
-size, -query-time
oracle for any constant . This matches, up to polylogarithmic factors, the
fastest failure-free distance oracles with nearly linear space. For single
vertex failures (), our -size,
-query-time oracle improves over the previously best
known tradeoff of Baswana et al. [SODA 2012] by polynomial factors for , . For multiple failures, no planarity exploiting
results were previously known
Cooperation and Competition when Bidding for Complex Projects: Centralized and Decentralized Perspectives
To successfully complete a complex project, be it a construction of an
airport or of a backbone IT system, agents (companies or individuals) must form
a team having required competences and resources. A team can be formed either
by the project issuer based on individual agents' offers (centralized
formation); or by the agents themselves (decentralized formation) bidding for a
project as a consortium---in that case many feasible teams compete for the
contract. We investigate rational strategies of the agents (what salary should
they ask? with whom should they team up?). We propose concepts to characterize
the stability of the winning teams and study their computational complexity
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