An O(EV log V) algorithm for finding a maximal weighted matching in general graphs
SIAM Journal on Computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Truthful approximation mechanisms for restricted combinatorial auctions: extended abstract
Eighteenth national conference on Artificial intelligence
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
Combinatorial Auctions: A Survey
INFORMS Journal on Computing
A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On complexity of single-minded auction
Journal of Computer and System Sciences
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Collusion-resistant mechanisms for single-parameter agents
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorial Auctions
Nash Stability in Additively Separable Hedonic Games Is NP-Hard
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
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We study the complexity issues for Walrasian equilibrium in a special case of combinatorial auction, called single-minded auction, in which every participant is interested in only one subset of commodities. Chen et al. [5] showed that it is NP-hard to decide the existence of a Walrasian equilibrium for a single-minded auction and proposed a notion of approximate Walrasian equilibrium called relaxed Walrasian equilibrium. We show that every single-minded auction has a $\frac{2}{3}$-relaxed Walrasian equilibrium proving a conjecture posed in [5]. Motivated by practical considerations, we introduce another concept of approximate Walrasian equilibrium called weak Walrasian equilibrium. We show it is strongly NP-complete to determine the existence of δ-weak Walrasian equilibrium, for any 0δ≤ 1. In search of positive results, we restrict our attention to the tollbooth problem [15], where every participant is interested in a single path in some underlying graph. We give a polynomial time algorithm to determine the existence of a Walrasian equilibrium and compute one (if it exists), when the graph is a tree. However, the problem is still hard for general graphs.