An Analysis of a Simple Algorithm for Random Derangements
نویسندگان
چکیده
We consider the uniform generation of random derangements, i.e., permutations without any fixed point. By using a rejection algorithm, we improve the straight-forward method of generating a random permutation until a derangement is obtained. This and our procedure are both linear with respect to the number of calls to the random generator, but we obtain an improvement of more than 36%. By using probability generating functions we perform an exact average analysis of the algorithm, showing that our approach is rather general and can be used to analyze random generation procedures based on the same rejection technique. Moreover, emphasis is given to combinatorial sums and a new interpretation of a known infinite lower triangular array is found.
منابع مشابه
Probability Generating Functions for Sattolo’s Algorithm
In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...
متن کاملAn Efficient Genetic Agorithm for Solving the Multi-Mode Resource-Constrained Project Scheduling Problem Based on Random Key Representation
In this paper, a new genetic algorithm (GA) is presented for solving the multi-mode resource-constrained project scheduling problem (MRCPSP) with minimization of project makespan as the objective subject to resource and precedence constraints. A random key and the related mode list (ML) representation scheme are used as encoding schemes and the multi-mode serial schedule generation scheme (MSSG...
متن کاملDesigning a new multi-objective fuzzy stochastic DEA model in a dynamic environment to estimate efficiency of decision making units (Case Study: An Iranian Petroleum Company)
This paper presents a new multi-objective fuzzy stochastic data envelopment analysis model (MOFS-DEA) under mean chance constraints and common weights to estimate the efficiency of decision making units for future financial periods of them. In the initial MOFS-DEA model, the outputs and inputs are characterized by random triangular fuzzy variables with normal distribution, in which ...
متن کاملUsing Non-Archimedean DEA Models for Classification of DMUs: A New Algorithm
A new algorithm for classification of DMUs to efficient and inefficient units in data envelopment analysis is presented. This algorithm uses the non-Archimedean Charnes-Cooper-Rhodes[1] (CCR) model. Also, it applies an assurance value for the non-Archimedean using only simple computations on inputs and outputs of DMUs (see [18]). The convergence and efficiency of the ne...
متن کاملAugmented Downhill Simplex a Modified Heuristic Optimization Method
Augmented Downhill Simplex Method (ADSM) is introduced here, that is a heuristic combination of Downhill Simplex Method (DSM) with Random Search algorithm. In fact, DSM is an interpretable nonlinear local optimization method. However, it is a local exploitation algorithm; so, it can be trapped in a local minimum. In contrast, random search is a global exploration, but less efficient. Here, rand...
متن کامل