We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp (Theoret. Comput. Sci., 2005) and by the current authors (Algorithmica, to appear). We prove that the minimum entropy orientation problem is NP-hard even if the ...

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a two-player game. We exhibit a class of two-player games having payoffs in the range [0, 1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n×n games, in the worst c...

We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfectly matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the subdomains where the emphasis is on the boundary values of the intermediate waves. This approach can be viewed as an effective approximation of an additive deco...

Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LP-relaxation. As extensions of the LP bound, we introduce novel general techniques proving formula size lower bounds, name...

A variant of the classical additive Schwarz preconditioner (AS) is presented and applied to the solution of a general class of twoand three-dimensional ̄ow problems. The scaled restricted additive Schwarz (RAS) with minimal overlap preconditioner is easy to parallelize since all the local communications among processors only involve information pertaining to the interface of the nonoverlapping ...

In this paper we are interested in bounding or calculating the additive functionals of the first return time on a set for discrete-time Markov chains on a countable state space, which is motivated by investigating ergodic theory and central limit theorems. To do so, we introduce the theory of the minimal nonnegative solution. This theory combined with some other techniques is proved useful for ...

In recent years, an algebraic framework was introduced for the analysis of convergence of Schwarz methods for the solution of linear systems of the form Ax = b. Within this framework, additive and multiplicative Schwarz were shown to converge when the coefficient matrix A is a nonsingular M -matrix, or a symmetric positive definite matrix. In this paper, these results are extended to the case o...

In this paper, we show that the additive Schwarz method proposed in [3] to solve one-obstacle problems converges in a much more general framework. We prove that this method can be applied to the minimization of functionals over a general enough convex set in a reflexive Banach space. In the Sobolev spaces, the proposed method is an additive Schwarz method for the solution of the variational ine...

The problem of nonlinear filtering with a non-Gaussian model of measurement errors is considered in this paper: Based on Bayes classification of the observations an approximate solution is introduced. The Bayesian estimator can be applied to any discrete time, lineal; or nonlinear system which is observed in additive non-Gaussian measurement noise. The problem of narrowband inte$erence suppress...

This paper presents an approximate multi-parametric quadratic programming approach to explicit solution of constrained linear MPC problems in the presence of bounded additive uncertainties, which is based on an orthogonal search tree structure of the state space partition. The explicit MPC controller minimizes the nominal value of the performance index and it is robust in the sense that all con...