Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Truth revelation in approximately efficient combinatorial auctions
Journal of the ACM (JACM)
An approximate truthful mechanism for combinatorial auctions with single parameter agents
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Truthful approximation mechanisms for restricted combinatorial auctions: extended abstract
Eighteenth national conference on Artificial intelligence
Reducing truth-telling online mechanisms to online optimization
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
FOCS '99 Proceedings of the 40th 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
Approximation techniques for utilitarian mechanism design
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Truthful and Near-Optimal Mechanism Design via Linear Programming
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Truthful Mechanisms via Greedy Iterative Packing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the limitations of Greedy mechanism design for truthful combinatorial auctions
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation Techniques for Utilitarian Mechanism Design
SIAM Journal on Computing
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The unsplittable flow problem is one of the most extensively studied optimization problems in the field of networking. An instance of it consists of an edge capacitated graph and a set of connection requests, each of which is associated with source and target vertices, a demand, and a value. The objective is to route a maximum value subset of requests subject to the edge capacities. It is a well known fact that as the capacities of the edges are larger with respect to the maximal demand among the requests, the problem can be approximated better. In particular, it is known that for sufficiently large capacities, the integrality gap of the corresponding integer linear program becomes 1+ε, which can be matched by an algorithm that utilizes the randomized rounding technique. In this paper, we focus our attention on the large capacities unsplittable flow problem in a game theoretic setting. In this setting, there are selfish agents, which control some of the requests characteristics, and may be dishonest about them. It is worth noting that in game theoretic settings many standard techniques, such as randomized rounding, violate certain monotonicity properties, which are imperative for truthfulness, and therefore cannot be employed. In light of this state of affairs, we design a monotone deterministic algorithm, which is based on a primal-dual machinery, which attains an approximation ratio of εε-1, up to a disparity of ε away. This implies an improvement on the current best truthful mechanism, as well as an improvement on the current best combinatorial algorithm for the problem under consideration. Surprisingly, we demonstrate that any algorithm in the family of reasonable iterative path minimizing algorithms, cannot yield a better approximation ratio. Consequently, it follows that in order to achieve a monotone PTAS, if exists, one would have to exert different techniques. We also consider the large capacities single-minded multi-unit combinatorial auction problem. This problem is closely related to the unsplittable flow problem since one can formulate it as a special case of the integer linear program of the unsplittable flow problem. Accordingly, we obtain a comparable performance guarantee by refining the algorithm suggested for the unsplittable flow problem.