Presorting algorithms: An average-case point of view

Presorting algorithms: An average-case point of view

We introduce the concept of presorting algorithms, quantifying and evaluating the performance of such algorithms with the average reduction in number of inversions. Stages of well-known algorithms such as Shellsort and quicksort are evaluated in such a framework and shown to cause a meaning drop in the inversion statistic. The expected value, variance and generating function for the decrease in...

A Personal View of Average-Case Complexity

The structural theory of average-case complexity , introduced by Levin , gives a formal setting for discussing the types of inputs for which a problem is diicult. This is vital to understanding both when a seemingly diicult (e.g. NP-complete) problem is actually easy on almost all instances , and to determining which problems might be suitable for applications requiring hard problems, such as c...

Interesting Case of Nephrocystosis, from an Obstetrical Point of View

Average Case Analysis of Marking Algorithms

The Lindstrom marking algorithm uses bounded workspace. Its time complexity is O(n) in all cases, but it has been assumed that the average case time complexity is O(n lg n). It is proven that the average case time complexity is Θ(n). Similarly, the average size of the Wegbreit bit stack is shown to be Θ(n).

Automatic Average { case Analysis of Algorithms

Many probabilistic properties of elementary discrete combinatorial structures of interest for the average{case analysis of algorithms prove to be decidable. This paper presents a general framework in which such decision procedures can be developed: It is based on a combination of generating function techniques for counting, and complex analysis techniques for asymptotic estimations. We expose h...