We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In particular, we demonstrate the strength of our techniques by exhibiting a lower bound of 2 - 1/m for the scheduling problem with unrelated machines (formulated as a mechanism design problem in the seminal paper of Nisan and Ronen on Algorithmic Mechanism Design). Our lower bound applies to truthful randomized mechanisms (disregarding any computational assumptions on the running time of these mechanisms). Moreover, it holds even for the weaker notion of truthfulness for randomized mechanisms - i.e., truth-fulness in expectation. This lower bound nearly matches the known 7/4 (randomized) truthful upper bound for the case of two machines (a non-truthful FPTAS exists). No lower bound for truthful randomized mechanisms in multi-parameter settings was previously known. We show an application of our techniques to the workload-minimization problem in networks. We prove our lower bounds for this problem in the inter-domain routing setting presented by Feigenbaum, Papadimitriou, Sami, and Shenker. Finally, we discuss several notions of non-utilitarian "fairness" (Max-Min fairness, Min-Max fairness, and envy minimization). We show how our techniques can be used to prove lower bounds for these notions.
|Original language||American English|
|Title of host publication||Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007|
|Publisher||Association for Computing Machinery|
|Number of pages||10|
|State||Published - 2007|
|Event||18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 - New Orleans, United States|
Duration: 7 Jan 2007 → 9 Jan 2007
|Name||Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms|
|Conference||18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007|
|Period||7/01/07 → 9/01/07|
Bibliographical noteFunding Information:
Supported by grants from the Israel Science Foundation and the USA Israel Bi-national Science Foundation.
Copyright © 2007 by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics.