On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The complexity of economic equilibria for house allocation markets
Information Processing Letters
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges
Proceedings of the 8th ACM conference on Electronic commerce
Improved approximation results for the stable marriage problem
ACM Transactions on Algorithms (TALG)
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Housing Markets Through Graphs
Algorithmica - Special Issue: Matching Under Preferences; Guest Editors: David F. Manlove, Robert W. Irving and Kazuo Iwama
An efficient implementation of the equilibrium algorithm for housing markets with duplicate houses
Information Processing Letters
Pareto optimality in house allocation problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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In a modification of the classical model of housing market which includes duplicate houses, economic equilibrium might not exist. As a measure of approximation the value sat $\mathcal(M)$ was proposed: the maximum number of satisfied agents in the market $\mathcal(M)$, where an agent is said to be satisfied if, given a set of prices, he gets a most preferred house in his budget set. Clearly, market $\mathcal(M)$ admits an economic equilibrium if sat(M) is equal to the total number n of agents, but sat$\mathcal(M)$ is NP-hard to compute. In this paper we give a 2-approximation algorithm for sat$\mathcal(M)$ in the case of trichotomic preferences. On the other hand, we prove that sat$\mathcal(M)$ is hard to approximate within a factor smaller than 21/19, even if each house type is used for at most two houses. If the preferences are not required to be trichotomic, the problem is hard to approximate within a factor smaller than 1.2. We also prove that, provided the Unique Games Conjecture is true, approximation is hard within a factor 1.25 for trichotomic preferences, and within a factor 1.5 in the case of general preferences.