Bayesian Truthful Mechanisms for Job Scheduling from Bi-criterion Approximation Algorithms [article]

Constantinos Daskalakis, S. Matthew Weinberg
2014 arXiv   pre-print
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of 2 and {m-k+1, Õ(√(k))} respectively, matching the approximation ratios of best known polynomial-time algorithms (for max-min fairness, the latter claim is true for certain ratios of the number of goods m to people k). Our mechanisms are obtained by establishing a polynomial-time
more » ... on-sensitive reduction from the problem of designing approximately optimal mechanisms for some arbitrary objective O to that of designing bi-criterion approximation algorithms for the same objective O plus a linear allocation cost term. Our reduction is itself enabled by extending the celebrated "equivalence of separation and optimization"[GLSS81,KP80] to also accommodate bi-criterion approximations. Moreover, to apply the reduction to the specific problems of makespan and max-min fairness we develop polynomial-time bi-criterion approximation algorithms for makespan minimization with costs and max-min fairness with costs, adapting the algorithms of [ST93], [BD05] and [AS07] to the type of bi-criterion approximation that is required by the reduction.
arXiv:1405.5940v1 fatcat:ujk7ymmuebff3ol376ptrgszqm