Related papers: Smoothed Complexity Theory
Spielman and Teng introduced the smoothed analysis of algorithms to provide a framework in which one could explain the success in practice of algorithms and heuristics that could not be understood through the traditional worst-case and…
Smoothed analysis is a method for analyzing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through worst-case analysis. Spielman and Teng…
We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small…
Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…
Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by…
Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak, STOC 2015; Larsen and…
The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
Smoothed analysis is a framework suggested for mediating gaps between worst-case and average-case complexities. In a recent work, Dinitz et al.~[Distributed Computing, 2018] suggested to use smoothed analysis in order to study dynamic…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
Narrowing the gap between theory and practice is a longstanding goal of the algorithm analysis community. To further progress our understanding of how algorithms work in practice, we propose a new algorithm analysis framework that we call…
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate…
We prove novel algorithmic guarantees for several online problems in the smoothed analysis model. In this model, at each time an adversary chooses an input distribution with density function bounded above by $\tfrac{1}{\sigma}$ times that…
We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics,…
We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum…
We perform a smoothed analysis of the termination phase of an interior-point method. By combining this analysis with the smoothed analysis of Renegar's interior-point algorithm by Dunagan, Spielman and Teng, we show that the smoothed…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an…