Joshua R. Wang

Minimizing Regret with Multiple Reserves

We study the problem of computing and learning non-anonymous reserve prices to maximize revenue. We first define the {\sc Maximizing Multiple Reserves (MMR)} problem in single-parameter matroid environments, where the input is

The Complexity of the k-means Method

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Deterministic Time-Space Trade-Offs for k-SUM.

valuation profiles v^1,...,v^m, indexed by the same n bidders, and the goal is to compute the vector r of (non-anonymous) reserve prices that maximizes the total revenue obtained on these profiles by the VCG mechanism with reserves r. We prove that the problem is APX-hard, even in the special case of single-item environments, and give a polynomial-time 1/2-approximation algorithm for it in arbitrary matroid environments. We then consider the online no-regret learning problem, and show how to exploit the special structure of the MMR problem to translate our offline approximation algorithm into an online learning algorithm that achieves asympototically time-averaged revenue at least 1/2 times that of the best fixed reserve prices in hindsight. On the negative side, we show that, quite generally, computational hardness for the offline optimization problem translates to computational hardness for obtaining vanishing time-averaged regret. Thus our hardness result for the MMR problem implies that computationally efficient online learning requires approximation, even in the special case of single-item auction environments.

Space-Efficient Randomized Algorithms for K-SUM

The k-means method is a widely used technique for clustering points in Euclidean space. While it is extremely fast in practice, its worst-case running time is exponential in the number of data points. We prove that the k-means method can implicitly solve PSPACE-complete problems, providing a complexity-theoretic explanation for its worst-case running time. Our result parallels recent work on the complexity of the simplex method for linear programming.

Cell-probe lower bounds from online communication complexity

Given a set of numbers, the

Approximation and fixed parameter subquadratic algorithms for radius and diameter in sparse graphs

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Finding four-node subgraphs in triangle time

-SUM problem asks for a subset of

Approximation and Fixed Parameter Subquadratic Algorithms for Radius and Diameter.

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Shuffles and Circuits: (On Lower Bounds for Modern Parallel Computation)

numbers that sums to zero. When the numbers are integers, the time and space complexity of

Approximation Bounds for Hierarchical Clustering: Average Linkage, Bisecting K-means, and Local Search

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