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Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
We study the data complexity of model-checking for logics with team semantics. We focus on dependence, inclusion, and independence logic formulas under both strict and lax team semantics. Our results delineate a clear…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
The following two decision problems capture the complexity of comparing integers or rationals that are succinctly represented in product-of-exponentials notation, or equivalently, via arithmetic circuits using only multiplication and…
The propositional planning problem is a notoriously difficult computational problem. Downey et al. (1999) initiated the parameterized analysis of planning (with plan length as the parameter) and B\"ackstr\"om et al. (2012) picked up this…
How hard is it to estimate a discrete-time signal $(x_{1}, ..., x_{n}) \in \mathbb{C}^n$ satisfying an unknown linear recurrence relation of order $s$ and observed in i.i.d. complex Gaussian noise? The class of all such signals is…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…
Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, e.g. in scheduling…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…
We consider the problem of approximating a smooth function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three…
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…