On designing truthful mechanisms for online scheduling

• Published in: Theoretical computer science Vol. 410; no. 36; pp. 3348 - 3356
• Main Authors: Auletta, Vincenzo, De Prisco, Roberto, Penna, Paolo, Persiano, Giuseppe
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 31.08.2009
• Subjects: Mechanism design; Online algorithms; Online truthful mechanisms; Scheduling; Online algorithms; Scheduling; Mechanism design; Online truthful mechanisms
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2008.12.057

We study the online version of the scheduling problem Q∥Cmax involving selfish agents, considered by Archer and Tardos in [A. Archer, E. Tardos, Truthful mechanisms for one-parameter agents, in: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS), 2001, pp. 482–491], where jobs must be scheduled on m related machines, each of them owned by a different selfish agent. We present a general technique for transforming competitive online algorithms for Q∥Cmax into truthful online mechanisms with a small loss of competitiveness. We also investigate the issue of designing new online algorithms from scratch so as to obtain efficient competitive mechanisms, and prove some lower bounds on a class of “natural” algorithms. A “direct” use of such natural algorithms to construct truthful mechanisms yields only trivial upper bounds for the case of two machines. Finally, we consider mechanisms with verification, introduced by Nisan and Ronen [N. Nisan, A. Ronen, Algorithmic mechanism design, in: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, STOC, 1999, pp. 129–140], for offline scheduling problems. We present the first constant-competitive online truthful mechanism with verification for any number of machines.