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Truthful optimization using mechanisms with verification
Theoretical Computer Science
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In this paper we study optimization problems with verifiableone-parameter selfish agents introduced by Auletta et al. [V.Auletta, R. De Prisco, P. Penna, P. Persiano, The power ofverification for one-parameter agents, in: Proceedings of the 31stInternational Colloquium on Automata, Languages and Programming,ICALP, in: LNCS, vol. 3142, 2004, pp. 171-182]. Our goal is toallocate load among the agents, provided that the secret data ofeach agent is a single positive real number: the cost they incurper unit load. In such a setting the payment is given after theload completion, therefore if a positive load is assigned to anagent, we are able to verify if the agent declared to be fasterthan she actually is. We design truthful mechanisms when theagents' type sets are upper-bounded by a finite value. We provide atruthful mechanism that is c·(1+ε)-approximate ifthe underlying algorithm is c-approximate and weakly-monotone.Moreover, if type sets are also discrete, we provide atruthful mechanism preserving the approximation ratio of itsalgorithmic part. Our results improve the existing ones whichprovide truthful mechanisms dealing only with finite type sets anddo not preserve the approximation ratio of the underlyingalgorithm. Finally, we give applications for our payment schemes.Firstly, we give a full characterization of theQ‖Cmax problem by using ourtechniques. Even if our payment schemes need upper-bounded typesets, every instance of Q‖Cmax canbe "mapped" into an instance with upper-bounded type setspreserving the approximation ratio. In conclusion, we turn ourattention to binary demand games. In particular, we show that theMinimum Radius Spanning Tree admits an exact truthful mechanismwith verification achieving time (and space) complexity of thefastest centralized algorithm for it. This contrasts with a recenttruthful mechanism for the same problem [G. Proietti, P. Widmayer,A truthful mechanism for the non-utilitarian minimum radiusspanning tree problem, in: Proceedings of the 17th ACM Symposium onParallelism in Algorithms and Architectures, SPAA, ACM Press, 2005,pp. 195-202] which pays a linear factor with respect to thecomplexity of the fastest centralized algorithm. Such a result isextended to several binary demand games studied in literature.