Kraft D., Fadaei S., Bichler M. (2014) Fast Convex Decomposition for Truthful Social Welfare Approximation. In: Liu TY., Qi Q., Ye Y. (eds) Web and Internet Economics. WINE 2014. Lecture Notes in Computer Science, vol 8877. Springer, Cham
Approximating the optimal social welfare while preserving truthfulness is a well studied problem in algorithmic mechanism design. Assuming that the social welfare of a given mechanism design problem can be optimized by an integer program whose integrality gap is at most α, Lavi and Swamy  propose a general approach to designing a randomized α-approximation mechanism which is truthful in expectation. Their method is based on decomposing an optimal solution for the relaxed linear program into a convex combination of integer solutions. Unfortunately, Lavi and Swamy’s decomposition technique relies heavily on the ellipsoid method, which is notorious for its poor practical performance. To overcome this problem, we present an alternative decomposition technique which yields an α(1 + ε) approximation and only requires a quadratic number of calls to an integrality gap verifier.
Convex decomposition Truthful in expectation Mechanism design Approximation algorithms