Optimal Lower Bounds for Anonymous Scheduling Mechanisms

Ashlagi, Itai; Dobzinski, Shahar; Lavi, Ron

doi:10.1287/moor.1110.0534

Cited by 46 publications

(59 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We denote an optimal solution 6 to the above LP by α LP (t), and the optimal objective value by µ LP t (dropping the LP superscript whenever this is clear from the context). The vector α LP (t) 5 Use the tail inequality Pr [X ≤ (1 − δ)µ] ≤ e − δ 2 2 µ where X is the number of tasks that are allocated to machine i = 1, µ = n 1 2 − 1 2n 2 , and choose δ ≤ n − 1 3 . 6 Notice that although µ LP t is unique, there might be various allocation fractions αi,j that give rise to the optimal makespan µ LP t , in which case we can choose an arbitrary one for α LP t , e.g.…”

Section: The Lp Mechanismmentioning

confidence: 99%

The anarchy of scheduling without money

Giannakopoulos

Koutsoupias

Kyropoulou

2019

Theoretical Computer Science

View full text Add to dashboard Cite

We consider the scheduling problem on n strategic unrelated machines when no payments are allowed, under the objective of minimizing the makespan. We adopt the model introduced in [Koutsoupias 2014] where a machine is bound by her declarations in the sense that if she is assigned a particular job then she will have to execute it for an amount of time at least equal to the one she reported, even if her private, true processing capabilities are actually faster. We provide a (non-truthful) randomized algorithm whose pure Price of Anarchy is arbitrarily close to 1 for the case of a single task and close to n if it is applied independently to schedule many tasks, which is asymptotically optimal for the natural class of anonymous, task-independent algorithms. Previous work considers the constraint of truthfulness and proves a tight approximation ratio of (n + 1)/2 for one task which generalizes to n(n + 1)/2 for many tasks. Furthermore, we revisit the truthfulness case and reduce the latter approximation ratio for many tasks down to n, asymptotically matching the best known lower bound. This is done via a detour to the relaxed, fractional version of the problem, for which we are also able to provide an optimal approximation ratio of 1. Finally, we mention that all our algorithms achieve optimal ratios of 1 for the social welfare objective.function that measures the quality of the outcome, the challenge is to design mechanisms which are able to elicit a desired behaviour from the players, while at the same time optimizing that objective value. A primary designer goal that has been extensively studied is that of truthfulness, under the central solution concept of dominant strategies: a player should be able to optimize her own individual utility by reporting truthfully, no matter what strategies the other players follow. However, achieving this is not always compatible with maintaining a good objective value [15,31]. The introduction of payments was suggested as a means towards achieving these goals, since a carefully designed payment scheme incentivizes the players to make truthful declarations. The goal now becomes to design such algorithms (termed mechanisms) which utilize monetary compensations in order to impose truthful behaviour while optimizing the objective function. A prominent positive result exists for utilitarian settings at which the objective function is the social welfare, where the well-known VCG mechanism [9, 16, 33] constitutes such an optimal mechanism. The study of the algorithmic aspect of mechanism design was initiated by Nisan and Ronen [26], and since then a significant body of work has been dedicated to optimization problems from the mechanism design point of view (see e.g. [4,10,21]).There are many situations, though, where the use of payments might be considered unethical [27], illegal (e.g. organ donations) or even just impractical. For this reason researchers have started turning their attention to possible ways of achieving truthfulness without the use of payments. In such a setting, in ord...

show abstract

Section: The Lp Mechanismmentioning

confidence: 99%

The anarchy of scheduling without money

Giannakopoulos

Koutsoupias

Kyropoulou

2019

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…However, truthful mechanisms have only been obtained with ratios of O(m) [Lu and Yu 2008a,b;Lu 2009], while only a lower bound of 2.61 has yet been proven [Christodoulou et al 2009;Koutsoupias and Vidali 2013]. The upper bound of O(m) is tight for the special case of anonymous mechanisms [Ashlagi et al 2012]. For the fractional problem, a (1 + (n − 1)/2)-approximative mechanism exists [Christodoulou et al 2010].…”

Section: Related Workmentioning

confidence: 99%

Truthful mechanism design via correlated tree rounding

et al. 2016

View full text Add to dashboard Cite

One of the most powerful algorithmic techniques for truthful mechanism design are maximal-indistributional-range (MIDR) mechanisms. Unfortunately, many algorithms using this paradigm rely on heavy algorithmic machinery and require the ellipsoid method or (approximate) solution of convex programs. In this paper, we present a simple and natural correlated rounding technique for designing mechanisms that are truthful in expectation. Our technique is elementary and can be implemented quickly. The main property we rely on is that the domain offers fractional optimum solutions with a tree structure.In auctions based on the generalized assignment problem, each bidder has a publicly known knapsack constraint that captures the subsets of items that are of value to him. He has a private valuation for each item and strives to maximize the value of assigned items minus payment. For this domain we design a mechanism for social welfare maximization. Our technique gives a truthful 2-approximate MIDR mechanism without using the ellipsoid method or convex programming. In contrast to some previous work, our mechanism achieves exact truthfulness.In restricted-related scheduling with selfish machines, each job comes with a public weight, and it must be assigned to a machine from a public job-specific subset. Each machine has a private speed and strives to maximize payments minus workload of jobs assigned to it. For this domain we design a mechanism for makespan minimization. Although this is a single-parameter domain, the approximation status of the underlying optimization problem is similar to unrelated scheduling: The best known algorithm gives a (nontruthful) 2-approximation for unrelated machines, and there is 1.5-hardness. Our mechanism matches this bound and provides a truthful 2-approximation.

show abstract

“…Every feasible solution corresponds to some amount of work allocated to each agent, and every agent has a private cost per unit of work which is either L (low) or H (high). 2 Typically the amount of work allocated to the agents cannot be arbitrary, but it is rather determined by the "combinatorial structure" of the problem under consideration. For instance, in the path auction problem [22], the mechanism must select a path in a graph, and each agent owns one edge of the graph (see Figure 1).…”

Section: Our Contributionmentioning

confidence: 99%

Bribeproof Mechanisms for Two-Values Domains

Mihaľák

Penna

Widmayer

2016

Algorithmic Game Theory

View full text Add to dashboard Cite

Schummer [28] introduced the concept of bribeproof mechanism which, in a context where monetary transfer between agents is possible, requires that manipulations through bribes are ruled out. Unfortunately, in many domains, the only bribeproof mechanisms are the trivial ones which return a fixed outcome.This work presents one of the few constructions of non-trivial bribeproof mechanisms for this setting. Though the suggested construction applies to rather restricted domains, the results obtained are tight: for several natural problems, the method yields the only possible bribeproof mechanism and no such mechanism is possible on more general domains.

show abstract

Optimal Lower Bounds for Anonymous Scheduling Mechanisms

Cited by 46 publications

References 15 publications

The anarchy of scheduling without money

The anarchy of scheduling without money

Truthful mechanism design via correlated tree rounding

Bribeproof Mechanisms for Two-Values Domains

Contact Info

Product

Resources

About