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Fast payment schemes for truthful mechanisms with verification

Fast payment schemes for truthful mechanisms with verification
Fast payment schemes for truthful mechanisms with verification
In this paper we study optimization problems with verifiable one-parameter selfish agents introduced by Auletta et al. [V. Auletta, R. De Prisco, P. Penna, P. Persiano, The power of verification for one-parameter agents, in: Proceedings of the 31st International Colloquium on Automata, Languages and Programming, ICALP, in: LNCS, vol. 3142, 2004, pp. 171–182]. Our goal is to allocate load among the agents, provided that the secret data of each agent is a single positive real number: the cost they incur per unit load. In such a setting the payment is given after the load completion, therefore if a positive load is assigned to an agent, we are able to verify if the agent declared to be faster than she actually is. We design truthful mechanisms when the agents’ type sets are upper-bounded by a finite value. We provide a truthful mechanism that is cdot operator(1+epsilon (Porson))-approximate if the underlying algorithm is c-approximate and weakly-monotone. Moreover, if type sets are also discrete, we provide a truthful mechanism preserving the approximation ratio of its algorithmic part. Our results improve the existing ones which provide truthful mechanisms dealing only with finite type sets and do not preserve the approximation ratio of the underlying algorithm. Finally, we give applications for our payment schemes. Firstly, we give a full characterization of the View the MathML source problem by using our techniques. Even if our payment schemes need upper-bounded type sets, every instance of View the MathML source can be “mapped” into an instance with upper-bounded type sets preserving the approximation ratio. In conclusion, we turn our attention to binary demand games. In particular, we show that the Minimum Radius Spanning Tree admits an exact truthful mechanism with verification achieving time (and space) complexity of the fastest centralized algorithm for it. This contrasts with a recent truthful mechanism for the same problem [G. Proietti, P. Widmayer, A truthful mechanism for the non-utilitarian minimum radius spanning tree problem, in: Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA, ACM Press, 2005, pp. 195–202] which pays a linear factor with respect to the complexity of the fastest centralized algorithm. Such a result is extended to several binary demand games studied in literature.
886-899
Ferrante, Alessandro
99ea0670-b674-4862-9656-64a1ee3d4401
Parlato, Gennaro
c28428a0-d3f3-4551-a4b5-b79e410f4923
Sorrentino, Francesco Sorrentino
0e421e56-f825-4cb0-b7cb-7b0b02019dfb
Ventre, Carmine
9abfa84f-266a-4296-82f1-ae3bdecaea38
Ferrante, Alessandro
99ea0670-b674-4862-9656-64a1ee3d4401
Parlato, Gennaro
c28428a0-d3f3-4551-a4b5-b79e410f4923
Sorrentino, Francesco Sorrentino
0e421e56-f825-4cb0-b7cb-7b0b02019dfb
Ventre, Carmine
9abfa84f-266a-4296-82f1-ae3bdecaea38

Ferrante, Alessandro, Parlato, Gennaro, Sorrentino, Francesco Sorrentino and Ventre, Carmine (2009) Fast payment schemes for truthful mechanisms with verification. Theoretical Computer Science, 410 (8-10), 886-899.

Record type: Article

Abstract

In this paper we study optimization problems with verifiable one-parameter selfish agents introduced by Auletta et al. [V. Auletta, R. De Prisco, P. Penna, P. Persiano, The power of verification for one-parameter agents, in: Proceedings of the 31st International Colloquium on Automata, Languages and Programming, ICALP, in: LNCS, vol. 3142, 2004, pp. 171–182]. Our goal is to allocate load among the agents, provided that the secret data of each agent is a single positive real number: the cost they incur per unit load. In such a setting the payment is given after the load completion, therefore if a positive load is assigned to an agent, we are able to verify if the agent declared to be faster than she actually is. We design truthful mechanisms when the agents’ type sets are upper-bounded by a finite value. We provide a truthful mechanism that is cdot operator(1+epsilon (Porson))-approximate if the underlying algorithm is c-approximate and weakly-monotone. Moreover, if type sets are also discrete, we provide a truthful mechanism preserving the approximation ratio of its algorithmic part. Our results improve the existing ones which provide truthful mechanisms dealing only with finite type sets and do not preserve the approximation ratio of the underlying algorithm. Finally, we give applications for our payment schemes. Firstly, we give a full characterization of the View the MathML source problem by using our techniques. Even if our payment schemes need upper-bounded type sets, every instance of View the MathML source can be “mapped” into an instance with upper-bounded type sets preserving the approximation ratio. In conclusion, we turn our attention to binary demand games. In particular, we show that the Minimum Radius Spanning Tree admits an exact truthful mechanism with verification achieving time (and space) complexity of the fastest centralized algorithm for it. This contrasts with a recent truthful mechanism for the same problem [G. Proietti, P. Widmayer, A truthful mechanism for the non-utilitarian minimum radius spanning tree problem, in: Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA, ACM Press, 2005, pp. 195–202] which pays a linear factor with respect to the complexity of the fastest centralized algorithm. Such a result is extended to several binary demand games studied in literature.

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Published date: 2009
Organisations: Electronic & Software Systems

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Local EPrints ID: 272458
URI: http://eprints.soton.ac.uk/id/eprint/272458
PURE UUID: c64a705c-0ea3-46d2-a175-fd0ed2209d81

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Date deposited: 13 Jun 2011 14:00
Last modified: 14 Mar 2024 10:01

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Contributors

Author: Alessandro Ferrante
Author: Gennaro Parlato
Author: Francesco Sorrentino Sorrentino
Author: Carmine Ventre

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