Yun Kuen Cheung

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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)
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 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)
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)
Consider the following weighted digital sum (WDS) variant: write integer n as n = 21 + 22 + · · · + 2k with i1 > i2 > · · · > ik ≥ 0 and set WM (n) := ∑k t=1 t 2t . This type of weighted digital sum arises (when M = 1) in the analysis of bottom-up mergesort but is not “smooth” enough to permit a clean analysis. We therefore analyze its average TWM (n) := 1(More)