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Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.


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Book ChapterDOI
20 Sep 2004
TL;DR: By viewing random 3-SAT as a distributional problem, this work goes over some of the notions of average-case complexity that were considered in the literature and notes that for dense formulas the problem is polynomial-time on average in the sense of Levin.
Abstract: By viewing random 3-SAT as a distributional problem, we go over some of the notions of average-case complexity that were considered in the literature. We note that for dense formulas the problem is polynomial-time on average in the sense of Levin. For sparse formulas the question remains widely open despite several recent attempts.
Journal ArticleDOI
TL;DR: A parallel algorithm with time complexity O(log n) for finding an ε-good colouring in the set balancing problem is proposed for parallel random access machines (PRAM) with polynomial number of processors.
Abstract: A parallel algorithm with time complexity O(log n) for finding an ε-good colouring in the set balancing problem is proposed for parallel random access machines (PRAM) with polynomial number of processors. The previously known parallel algorithms proposed independently in [3, 4] have the time complexity Ο (log n).
Journal Article
TL;DR: In this paper, a hierarchy of counting complexity classes #@?Opt"kP with k>=1 corresponding to all levels of the polynomial hierarchy is introduced, and several important properties of these new classes are proved.
Abstract: Following the approach of Hemaspaandra and Vollmer, we can define counting complexity classes #@?C for any complexity class C of decision problems. In particular, the classes #@?@P"kP with k>=1 corresponding to all levels of the polynomial hierarchy, have thus been studied. However, for a large variety of counting problems arising from optimization problems, a precise complexity classification turns out to be impossible with these classes. In order to remedy this unsatisfactory situation, we introduce a hierarchy of new counting complexity classes #@?Opt"kP and #@?Opt"kP[logn] with k>=1. We prove several important properties of these new classes, like closure properties and the relationship with the #@?@P"kP-classes. Moreover, we establish the completeness of several natural counting complexity problems for these new classes.
Journal ArticleDOI
TL;DR: This paper attempts to compute the complexity of Optimized Power Set Computational algorithm (OPCA), found to be in the order of 2 n.
Abstract: This paper attempts to compute the complexity of Optimized Power Set Computational algorithm (OPCA). The algorithmic complexity has been found to be in the order of 2 n .
Posted Content
TL;DR: It is proved that tractability of an LMP in Λ std is equivalent to tractability in Κ all, although the proof is no(constructive), and the optimal design problem for an L MP is addressed by using a relation to the worst case setting.
Abstract: We study the average case complexity of a linear multivariate problem $(\lmp)$ defined on functions of $d$ variables. We consider two classes of information. The first $\lstd$ consists of function values and the second $\lall$ of all continuous linear functionals. Tractability of $\lmp$ means that the average case complexity is $O((1/\e)^p)$ with $p$ independent of $d$. We prove that tractability of an $\lmp$ in $\lstd$ is equivalent to tractability in $\lall$, although the proof is {\it not} constructive. We provide a simple condition to check tractability in $\lall$. We also address the optimal design problem for an $\lmp$ by using a relation to the worst case setting. We find the order of the average case complexity and optimal sample points for multivariate function approximation. The theoretical results are illustrated for the folded Wiener sheet measure.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
20216
202010
20199
201810
201732