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We provide a duality-based framework for revenue maximization in a multiple-good monopoly. Our framework shows that every optimal mechanism has a certificate of optimality, taking the form of an optimal transportation map between measures. Using our framework, we prove that grand-bundling mechanisms are optimal if and only if two stochastic dominance… (More)

Optimal mechanisms have been provided in quite general multi-item settings [Cai et al. 2012b, as long as each bidder's type distribution is given explicitly by listing every type in the support along with its associated probability. In the implicit setting, e.g. when the bidders have additive valuations with independent and/or continuous values for the… (More)

- Dimitris Fotakis, Christos Tzamos
- Theor. Comput. Sci.
- 2010

We study Facility Location games, where a number of facilities are placed in a metric space based on locations reported by strategic agents. A mechanism maps the agents’ locations to a set of facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We… (More)

We provide global convergence guarantees for the expectation-maximization (EM) algorithm applied to mixtures of two Gaussians with known covariance matrices. We show that EM converges geometrically to the correct mean vectors, and provide simple, closed-form expressions for the convergence rate. As a simple illustration, we show that in one dimension ten… (More)

Myerson’s seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders [17]. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a… (More)

An (<i>n</i>,<i>k</i>)-<em>Poisson Multinomial Distribution</em> (PMD) is the distribution of the sum of <i>n</i> independent random vectors supported on the set <b> </b><i>B</i><sub><i>k</i></sub>={<i>e</i><sub>1</sub>,…,<i>e</i><sub><i>k</i></sub>} of standard basis vectors in ℝ<sup><i>k</i></sup>. We show that any… (More)

- Constantinos Daskalakis, Gautam Kamath, Christos Tzamos
- 2015 IEEE 56th Annual Symposium on Foundations of…
- 2015

An (n, k)-Poisson Multinomial Distribution (PMD) is the distribution of the sum of n independent random vectors supported on the set Bk={e<sub>1</sub>,...,ek} of standard basis vectors in R<sup>k</sup>. We prove a structural characterization of these distributions, showing that, for all ε > 0, any (n, k)-Poisson multinomial random vector is… (More)

- Arturs Backurs, Nishanth Dikkala, Christos Tzamos
- ICALP
- 2016

Given n weighted points (positive or negative) in d dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains? The best known algorithm for this problem is based on a reduction to a related problem, the Weighted Depth problem [Chan, FOCS, 2013], and runs in time O(n). It was conjectured [Barbay et al., CCCG, 2013]… (More)

- Arturs Backurs, Christos Tzamos
- ICML
- 2017

The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time O(Tn) given a sequence of T observations from a HMM with n states. Despite significant interest in the problem and prolonged effort by different communities, no known algorithm achieves more than a… (More)

- Dimitris Fotakis, Christos Tzamos
- ACM Trans. Economics and Comput.
- 2013

We consider <i>K</i>-Facility Location games, where <i>n</i> strategic agents report their locations in a metric space and a mechanism maps them to <i>K</i> facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in deterministic… (More)