Exact arborescences, matchings and cycles
Discrete Applied Mathematics
Random pseudo-polynomial algorithms for exact matroid problems
Journal of Algorithms
Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Truth revelation in approximately efficient combinatorial auctions
Journal of the ACM (JACM)
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Truthful approximation mechanisms for restricted combinatorial auctions: extended abstract
Eighteenth national conference on Artificial intelligence
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Incentive compatible multi unit combinatorial auctions
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Approximation techniques for utilitarian mechanism design
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Truthful and Near-Optimal Mechanism Design via Linear Programming
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Truthful randomized mechanisms for combinatorial auctions
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Mechanisms for multi-unit auctions
Proceedings of the 8th ACM conference on Electronic commerce
Designing a truthful mechanism for a spanning arborescence bicriteria problem
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
Approximation Techniques for Utilitarian Mechanism Design
SIAM Journal on Computing
Efficiency-revenue trade-offs in auctions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Mechanisms for multi-unit combinatorial auctions with a few distinct goods
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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In a classic optimization problem the complete input data is known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In case of NP-hard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multi-objective optimization problems, where we are given the main objective function, and a set of secondary objectives which are modeled via budget constraints. Multi-objective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting, goals. Our main contribution is showing that two of the main tools for the design of approximation algorithms for multi-objective optimization problems, namely approximate Pareto curves and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto curves, we devise truthful FPTASs for multi-objective optimization problems whose exact version admits a pseudo-polynomial-time algorithm, as for instance the multi-budgeted versions of minimum spanning tree, shortest path, maximum (perfect) matching, and matroid intersection. Our technique applies also to multi-dimensional knapsack and multi-unit combinatorial auctions. Our FPTASs compute a (1 + ε)-approximate solution violating each budget constraint by a factor (1 + ε). For a relevant sub-class of the mentioned problems we also present a PTAS (not violating any constraint), which combines the approach above with a novel monotone way to guess the heaviest elements in the optimum solution. Finally we present a universally truthful Las Vegas PTAS for minimum spanning tree with a single budget constraint. This result is based on the Lagrangian relaxation method, in combination with our monotone guessing step and a random perturbation step (ensuring low expected running time in a way similar to the smoothed analysis of algorithms). All the mentioned results match the best known approximation ratios, which however are obtained by non-truthful algorithms.