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Tatonnement is a simple and natural rule for updating prices in Exchange (Arrow-Debreu) markets. In this paper we define a class of markets for which tatonnement is equivalent to gradient descent. This is the class of markets for which there is a convex potential function whose gradient is always equal to the negative of the excess demand and we call it… (More)

This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities.
The current work… (More)

This paper studies two functions arising separately in the analysis of algorithms. The first function is the solution to the Multidimensional Divide-And-Conquer (MDC) Recurrence that arises when solving problems involving points in d-dimensional space. The second function concerns weighted digital sums. Let n = (bibi−1 · · · b1b0)2 and SM (n) = i t=0 t(t +… (More)

Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been studied since the 1980s, and they have been experiencing a resurgence due to demand from large-scale machine learning… (More)

Given a graph where vertices are partitioned into k terminals and non-terminals, the goal is to compress the graph (i.e., reduce the number of non-terminals) using minor operations while preserving terminal distances approximately. The distortion of a compressed graph is the maximum multiplicative blow-up of distances between all pairs of terminals. We… (More)

This paper concerns asynchrony in iterative processes, focusing on gradient descent and tatonnement, a fundamental price dynamic. Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process, although distributed and asynchronous variants have been… (More)

We revisit the problem of designing strategyproof mechanisms for allocating divisible items among two agents who have linear utilities, where payments are disallowed and there is no prior information on the agents' preferences. The objective is to design strategyproof mechanisms which are competitive against the most efficient (but not strategyproof)… (More)

Combinatorial auctions (CA) are a well-studied area in algorithmic mechanism design. However, contrary to the standard model, empirical studies suggest that a bidder's valuation often does not depend solely on the goods assigned to him. For instance, in adwords auctions an advertiser might not want his ads to be displayed next to his competitors' ads. In… (More)

- Yun Kuen Cheung, Xi Chen, Jeff Kahn, Subhash Khot, Swastik Kopparty, Michael Saks +1 other
- 2014

This dissertation is dedicated to all eggs that break against the high and cold wall. iii Acknowledgements Counting from my first footstep in the Hong Kong University of Science and Technology (HKUST) as an university student, it has been rightly a decade for me to reach the milestone of completing this doctorate degree. This could not be possible with the… (More)

This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities. The current work… (More)