Improved lower bounds for non-utilitarian truthfulness

Abstract

We study the limitations imposed by truthfulness for two non-utilitarian multi-parameter optimization problems. The first is the workload minimization in inter-domain routing problem, and the other is the unrelated machines scheduling problem. Our main findings can be briefly summarized as follows: 1. We prove that any truthful deterministic mechanism and any universal truthful randomized mechanism for workload minimization in inter-domain routing cannot achieve approximation ratio better than 2. These results improve the current lower bounds of ( 1 + 5 ) / 2 ≈ 1.618 and ( 3 + 5 ) / 4 ≈ 1.309 due to Mu’alem and Schapira [A. Mu’alem, M. Schapira, Setting lower bounds on truthfulness, in: Proceedings 18th annual ACM-SIAM Symposium on Discrete Algorithms, 2007, pp. 1143–1152]. 2. We establish a lower bound of 1 + 2 ≈ 2.414 on the achievable approximation guarantee of any truthful deterministic mechanism for unrelated machines scheduling when the number of machines is at least 3. This lower bound is comparable to a recent result by Christodoulou, Koutsoupias and Vidali [G. Christodoulou, E. Koutsoupias, A. Vidali, A lower bound for scheduling mechanisms, in: Proceedings 18th annual ACM-SIAM Symposium on Discrete Algorithms, 2007, pp. 1163–1170].