Average case optimality for linear problems

A Survey of Average Case Complexity for Linear Multivariate Problems*

We survey recent results on the average case complexity for linear multivariate problems. Our emphasis is on problems defined on spaces of functions of d variables with large d. We present the sharp order of the average case complexity for a number of linear multivariate problems as well as necessary and sufficient conditions for the average case complexity not to be exponential in d. DOI: 10.3...

Average Case Complexity of Linear Multivariate Problems Part Ii: Applications

We apply the theoretical results of Part I to linear multivariate problems LMP equipped with the folded Wiener sheet measure. We are particularly interested in multivariate weighted integration and multivariate function approximation. We prove that any LMP which satisses (A.1) of Part I is tractable and its exponent is at most 2. We show that optimal or nearly optimal sample points can be deriv...

Fuzzy optimality relation for perceptive MDPs - the average case

This paper is a sequel to Kurano et al [9], [10], in which the fuzzy perceptive models for optimal stopping or discounted Markov decision process is given. We proposed a method of computing the corresponding fuzzy perceptive values. Here, we deal with the average case for Markov decision processes with fuzzy perceptive transition matrices and characterize the optimal average expected reward, ca...

Average - case analysis for combinatorial problems

This thesis considers the average case analysis of algorithms, focusing primarily on NP-hard combinatorial optimization problems. It includes a catalog of distributions frequently used in average-case analysis and a collection of mathematical tools that have been useful in studying these distributions. The bulk of the thesis consists of case-studies in average-case analysis of algorithms. Algor...

Average-Case Intractable NP Problems