On Parity based Divide and Conquer Recursive Functions
نویسنده
چکیده
The parity based divide and conquer recursion trees are introduced where the sizes of the tree do not grow monotonically as n grows. These non-monotonic recursive functions called fogk(n) and f̃ogk(n) are strictly less than linear, o(n) but greater than logarithm, Ω(logn). Properties of fogk(n) such as non-monotonicity, upper and lower bounds, etc. are examined and proven. These functions are useful to analyze computational complexities of certain algorithms, especially problems of finding various properties of k-ary divide and conquer trees or size balanced k-ary trees. Several integer sequences based on the divide and conquer recursive relations are newly discovered as well.
منابع مشابه
Exact Asymptotics of Divide-and-Conquer Recurrences
The divide-and-conquer principle is a majoi paradigm of algorithms design. Corresponding cost functions satisfy recurrences that directly reflect the decomposition mechanism used in the algorithm. This work shows that periodicity phenomena, often of a fractal nature, are ubiquitous in the performances of these algorithms. Mellin transforms and Dirichlet series are used to attain precise asympto...
متن کاملAn Improved Master Theorem for Divide-and-Conquer Recurrences
We present a new master theorem for the study of divide-and-conquer recursive deenitions, which improves the old one in several aspects. In particular, it provides more information, frees us from technicalities like oors and ceilings, and covers a wider set of toll functions and weight distributions, stochastic recurrences included.
متن کاملAnalysis of algorithms by the contraction method: additive and max-recursive sequences
In the first part of this paper we give an introduction to the contraction method for the analysis of additive recursive sequences of divide and conquer type. Recently some general limit theorems have been obtained by this method based on a general transfer theorem. This allows to conclude from the recursive structure and the asymptotics of first moment(s) the limiting distribution. In the seco...
متن کاملSolving Divide and Conquer Recurrences By Master Theorem á la Charlie
This paper discusses analysis of recursive problems. It delves first on their classification, and then the various methods of solving them, depending on which class the recursive relation belongs to. An improvement on the Master Method is then described and used to demonstrate how this method is used to solve recursive relations on Divide & Conquer problems. The revised method is found easier t...
متن کاملFree Vibration Analysis of Repetitive Structures using Decomposition, and Divide-Conquer Methods
This paper consists of three sections. In the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. In the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in ...
متن کامل