Truthful algorithms for scheduling selfish tasks on parallel machines

Abstract

International audienceWe consider the problem of designing truthful mechanisms for scheduling \em selfish tasks (or agents)-whose objective is the minimization of their completion times- on parallel identical machines in order to minimize the \em makespan. A truthful mechanism can be easily obtained in this context (if we, of course, assume that the tasks cannot shrink their lengths) by scheduling the tasks following the increasing order of their lengths. The quality of a mechanism is measured by its approximation factor (price of anarchy, in a distributed system) w.r.t. the social optimum. The previous mechanism, known as SPT, produces a $(2-1/m)$-approximate schedule, where $m$ is the number of machines. The central question in this paper is the following: \em ``Are there other truthful mechanisms with better approximation guarantee (price of anarchy) for the considered scheduling problem?'' This question has been raised by Christodoulou et al \citekoutsoupias in the context of coordination mechanisms, but it is also relevant in centrally controlled systems. We present (randomized) truthful mechanisms for both the centralized and the distributed settings that improve the (expected) approximation guarantee (price of anarchy) of the SPT mechanism. Our centralized mechanism holds for any number of machines and arbitrary schedule lengths, while the coordination mechanism holds only for two machines and schedule lengths that are powers of a certain constant

The price of stability in selfish scheduling games

“…Note that although the characteristic of the Nash solution derived from above does not depend on a particular sequencing policy used, the exact bound on the POS does. With Theorem 9, we obtain the following two POS results directly via the results on POA for identical machines, due respectively to [1] and [6]: Corollary 10. The price of stability in scheduling games with m identical machines using SPT sequencing policy is 2 − 1/m.…”

Resource trading in cloud environments for utility maximisation using game theoretic modelling approach

“…The problem of scheduling tasks on parallel identical machines is investigated in [12]. The main goal of the proposed scheme is to minimise the makespan (i.e.…”

Coordination mechanisms

“…In particular, [19,22] study coordination mechanisms for the selfish task allocation, while [2,8] consider truthful mechanisms for the same problem. Recently, Azar et al [5] and Caragiannis [6] consider coordination mechanisms for selfish scheduling on unrelated machines.…”