Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
Local search performance guarantees for restricted related parallel machine scheduling
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Task graph pre-scheduling, using Nash equilibrium in game theory
The Journal of Supercomputing
Altruism in Atomic Congestion Games
ACM Transactions on Economics and Computation
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We consider the problem of routing n users on m parallel links under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. So, this problem is equivalent to the correspondingly restricted scheduling problem of assigning n jobs to m parallel machines. In a Nash equilibrium, no user may improve its own Individual Cost (latency) by unilaterally switching to another link from its set of allowed links. For identical links, we present, as our main result, a polynomial time algorithm to compute from any given assignment a Nash equilibrium with non-increased makespan. The algorithm gradually transforms the assignment by pushing the unsplittable user traffics through a flow network, which is constructed from the users and the links. The algorithm uses ideas from blocking flows. Furthermore, we use techniques simular to those in the generic PreflowPush algorithm to approximate in polynomial time a schedule with optimum makespan. This results to an improved approximation factor of $2-\frac{1}{w_{1}}$for identical links, where w 1 is the largest user traffic, and to an approximation factor of 2 for related links.