On the complexity of edge traversing
Journal of the ACM (JACM)
Approximation Algorithms for Some Postman Problems
Journal of the ACM (JACM)
A 3/2-Approximation Algorithm for the Mixed Postman Problem
SIAM Journal on Discrete Mathematics
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network
Transportation Science
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Towards truthful mechanisms for binary demand games: a general framework
Proceedings of the 6th ACM conference on Electronic commerce
A truthful mechanism for the non-utilitarian minimum radius spanning tree problem
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Strongly polynomial-time truthful mechanisms in one shot
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Efficient truthful mechanisms for the single-source shortest paths tree problem
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
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Let G = (V, E) be a graph modeling a network where each edge is owned by a selfish agent, which establishes the cost for traversing her edge (i.e., assigns a weight to her edge) by pursuing only her personal utility. In such a setting, we aim at designing approximate truthful mechanisms for several NP-hard traversal problems on G, like the graphical traveling salesman problem, the rural postman problem, and the mixed Chinese postman problem, either of which asks for using an edge of G several times, in general. Thus, in game-theoretic terms, these are one-parameter problems, but with a peculiarity: the work load of each agent is a natural number. In this paper we refine the classic notion of monotonicity of an algorithm so as to exactly capture this property, and we then provide a general mechanism design technique that guarantees this monotonicity and that allows to compute efficiently the corresponding payments. In this way, we show that the former two problems and the latter one admit a 3/2- and a 2-approximate truthful mechanism, respectively. Thus, for the first two problems we match the best known approximation ratios holding for their corresponding centralized versions, while for the third one we are only a 4/3-factor away from it.