Noticias en español
Stability in Matrix Games.
Abstract: We consider the simplest game, Matrix Games, and basic stability questions on the value and strategies upon perturbations on the payoff matrix. Considering polynomial perturbations, we design polynomial-time algorithms for the following tasks: (a) ensuring that, for every sufficiently small error, there is a strategy to guarantee that the value is at least the value of the error-free case; (b) ensuring that there is a fixed strategy to guarantee that, for every sufficiently small error, the value is at least the value of the error-free case; and (c) computing the analytical form...
Read MorePopular Branchings and Their Dual Certificates.
Abstract: Let G be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed forests; a branching B is popular if B does not lose a head-to-head election (where nodes cast votes) against any branching. Such popular branchings have a natural application in liquid democracy. The popular branching problem is to decide if G admits a popular branching or not. We give a characterization of popular branchings in terms of dual certificates and use this characterization to design an efficient...
Read MoreImproved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More.
Abstract: In the 2-Dimensional Knapsack problem (2DK) we are given a square knapsack and a collection of n rectangular items with integer sizes and profits. Our goal is to find the most profitable subset of items that can be packed non-overlappingly into the knapsack. The currently best known polynomial-time approximation factor for 2DK is 17/9+eps<1.89 and there is a (3/2+eps)-approximation algorithm if we are allowed to rotate items by 90 degrees. In this talk, I will present a (4/3+eps)-approximation algorithms in polynomial time for both cases, assuming that all input data are...
Read MoreNon-Euclidean Differentially Private Stochastic Convex Optimization.
Abstract: Differentially private (DP) stochastic convex optimization (SCO) is a fundamental problem, where the goal is to approximately minimize the population risk with respect to a convex loss function, given a dataset of i.i.d. samples from a distribution, while satisfying differential privacy with respect to the dataset. Most of the existing works in the literature of private convex optimization focus on the Euclidean (i.e., $\ell_2$) setting, where the loss is assumed to be Lipschitz (and possibly smooth) w.r.t.~the $\ell_2$ norm over a constraint set with bounded $\ell_2$ diameter....
Read MoreThe Dispersion Time of Random Walks on Finite Graphs.
Abstract: Consider two random processes on an n vertex graph related to Internal Diffusion-Limited Aggregation (IDLA). In each process n particles perform independent random walks from a fixed vertex until they reach an unvisited vertex, at which point they settle. In the first process only one particle moves until settling and then the next starts, in the second process all particles are released together. We study the dispersion time which is the time taken for the longest walk to settle. We present a new coupling which allows us to compare dispersion time across the processes. We...
Read MoreStable matching games.
Abstract: Gale and Shapley (1962) introduced a matching problem between two sets of agents M and W, who need to be paired by taking into account that each agent on one side of the market has an exogenous preference order over the agents of the other side. They defined a matching as stable if no unmatched pair can both improve their payoffs by breaking their couples and forming a new one. They proved the existence of a stable matching using a deferred-acceptance algorithm. Shapley and Shubik (1971) extended the model by allowing monetary transfers. Our article offers a further extension by...
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