Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Truth revelation in approximately efficient combinatorial auctions
Journal of the ACM (JACM)
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
On the computational power of iterative auctions
Proceedings of the 6th ACM conference on Electronic commerce
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Combinatorial Auctions
Truthful and Near-Optimal Mechanism Design via Linear Programming
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Combinatorial auctions with k-wise dependent valuations
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Computationally feasible VCG mechanisms
Journal of Artificial Intelligence Research
On Maximizing Welfare When Utility Functions Are Subadditive
SIAM Journal on Computing
On the Power of Randomization in Algorithmic Mechanism Design
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
From convex optimization to randomized mechanisms: toward optimal combinatorial auctions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Welfare maximization and the supermodular degree
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Complements between goods--where one good takes on added value in the presence of another--have been a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications for combinatorial auctions, like spectrum license auctions. On the other, welfare maximization in the presence of complements is notoriously difficult, and this intractability has stymied theoretical progress in the area. For example, there are no known positive results for combinatorial auctions in which bidder valuations are multi-parameter and non-complement-free, other than the relatively weak results known for general valuations. To make inroads on the problem of combinatorial auction design in the presence of complements, we propose a model for valuations with complements that is parameterized by the "size" of the complements. The model permits a succinct representation, a variety of computationally efficient queries, and non-trivial welfare-maximization algorithms and mechanisms. Specifically, a hypergraph-r valuation v for a good set M is represented by a hypergraph H = (M,E), where every (hyper-)edge e -- E contains at most r vertices and has a nonnegative weight we. Each good j -- M also has a nonnegative weight wj. The value v(S) for a subset S ⊆ M of goods is defined as the sum of the weights of the goods and edges entirely contained in S. We design the following polynomial-time approximation algorithms and truthful mechanisms for welfare maximization with bidders with hypergraph valuations. (1) For bidders whose valuations correspond to subgraphs of a known graph that is planar (or more generally, excludes a fixed minor), we give a truthful and (1 + ∈)-approximate mechanism. (2) We give a polynomial-time, r-approximation algorithm for welfare maximization with hypergraph-r valuations. Our algorithm randomly rounds a compact linear programming relaxation of the problem. (3) We design a different approximation algorithm and use it to give a polynomial-time, truthful-inexpectation mechanism that has an approximation factor of O(logr m).