(pseudo)random number generator (RNG) usually refers to an algorithm used for step (1). In principle. 8, we cover non-uniform random variate generators. Computational complexity theory, under the familiar “rough-cut” assumption that. How To Generate Random Numbers In Excel Worksheets - Part II. Contents Non-Uniform Random Numbers - The Standard Excel Way. Non-Uniform Random Numbers - Using EasyFitXL Visual Random Number Generation Conclusion. Non-Uniform Random Numbers - The Standard Excel Way. EasyFitXL – Easily Fit. Replacing 0.2 with RAND will yield the Normal.
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Non-Uniform Random Variate Generation
'... This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorith ...'
Abstract - Cited by 1006 (25 self) - Add to MetaCart This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.
A new approach to the minimum cut problem
'... Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds th ...'
Abstract - Cited by 126 (9 self) - Add to MetaCart Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n 2 log 3 n) time, a significant improvement over the previous Õ(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in �� � with n 2 processors; this gives the first proof that the minimum cut problem can be solved in ���. The algorithm does more than find a single minimum cut; it finds all of them. With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of � of the minimum cut’s in expected Õ(n 2 � ) time, or in �� � with n 2 � processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected Õ(n 2(r�1) ) time, or in �� � with n 2(r�1) processors. The “trace ” of the algorithm’s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the
(Show Context)Boltzmann Samplers For The Random Generation Of Combinatorial Structures
'... This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combina ...'
Abstract - Cited by 107 (3 self) - Add to MetaCart This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class -- an object receives a probability essentially proportional to an exponential of its size. As demonstrated here, the resulting algorithms based on real-arithmetic operations often operate in linear time. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.
(Show Context)RANDOM SAMPLING IN CUT, FLOW, AND NETWORK DESIGN PROBLEMS
'... We use random sampling as a tool for solving undirected graph problems. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph’s edges will accurately approximate the value of all cuts in the original graph with high probability. This makes sampling effective for pro ...'
Abstract - Cited by 102 (12 self) - Add to MetaCart We use random sampling as a tool for solving undirected graph problems. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph’s edges will accurately approximate the value of all cuts in the original graph with high probability. This makes sampling effective for problems involving cuts in graphs. We present fast randomized (Monte Carlo and Las Vegas) algorithms for approximating and exactly finding minimum cuts and maximum flows in unweighted, undirected graphs. Our cut-approximation algorithms extend unchanged to weighted graphs while our weighted-graph flow algorithms are somewhat slower. Our approach gives a general paradigm with potential applications to any packing problem. It has since been used in a near-linear time algorithm for finding minimum cuts, as well as faster cut and flow algorithms. Our sampling theorems also yield faster algorithms for several other cut-based problems, including approximating the best balanced cut of a graph, finding a k-connected orientation of a 2k-connected graph, and finding integral multicommodity flows in graphs with a great deal of excess capacity. Our methods also improve the efficiency of some parallel cut and flow algorithms. Our methods also apply to the network design problem, where we wish to build a network satisfying certain connectivity requirements between vertices. We can purchase edges of various costs and wish to satisfy the requirements at minimum total cost. Since our sampling theorems apply even when the sampling probabilities are different for different edges, we can apply randomized rounding to solve network design problems. This gives approximation algorithms that guarantee much better approximations than previous algorithms whenever the minimum connectivity requirement is large. As a particular example, we improve the best approximation bound for the minimum k-connected subgraph problem from 1.85 to 1 � O(�log n)/k).
(Show Context)Approximations of General Independent Distributions
'... We describe efficient constructions of small probability spaces that approximate the independent distribution for general random variables. Previous work on efficient constructions concentrate on approximations of the independent distribution for the special case of uniform boolean-valued random var ...'
Abstract - Cited by 34 (5 self) - Add to MetaCart We describe efficient constructions of small probability spaces that approximate the independent distribution for general random variables. Previous work on efficient constructions concentrate on approximations of the independent distribution for the special case of uniform boolean-valued random variables. Our results yield efficient constructions of small sets with low discrepancy in high dimensional space and have applications to derandomizing randomized algorithms. 1 Introduction The problem of constructing small sample spaces that "approximate" the independent distribution on n random variables has received considerable attention recently (cf. [6, Chor Goldreich] [8, Karp Wigderson], [11, Luby], [1, Alon Babai Itai], [13, Naor Naor], [2, Alon Goldreich Hastad Peralta], [3, Azar Motwani Naor]). The primary motivation for this line of research is that random variables that are "approximately" independent suffices for the analysis of many interesting randomized algorithm and hence c...
On the Information Rate of Secret Sharing Schemes
'... We derive new limitations on the information rate and the average information rate of secret sharing schemes for access structure represented by graphs. We give the first proof of the existence of access structures with optimal information rate and optimal average information rate less that 1=2 + ff ...'
![The Complexity Of Nonuniform Random Number Generation Pdf Download The Complexity Of Nonuniform Random Number Generation Pdf Download](http://www.nature.com/article-assets/npg/srep/2016/160519/srep26222/images/m685/srep26222-f5.jpg)
We derive new limitations on the information rate and the average information rate of secret sharing schemes for access structure represented by graphs. We give the first proof of the existence of access structures with optimal information rate and optimal average information rate less that 1=2 + ffl, where ffl is an arbitrary positive constant. We also consider the problem of testing if one of these access structures is a sub-structure of an arbitrary access structure and we show that this problem is NP-complete. We provide several general lower bounds on information rate and average information rate of graphs. In particular, we show that any graph with n vertices admits a secret sharing scheme with information rateOmegaGammate/3 n)=n). 1 Introduction A secret sharing scheme is a method to distribute a secret s among a set of participants P in such a way that only qualified subsets of P can reconstruct the value of s whereas any other subset of P ; non-qualified to know s; cannot ...
On universal types
'... We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978 ...'
Abstract - Cited by 25 (6 self) - Add to MetaCart![The complexity of nonuniform random number generation pdf download free The complexity of nonuniform random number generation pdf download free](/uploads/1/2/5/8/125824456/989840419.png)
We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978). We show that the empirical probability distributions of any finite order of two sequences of the same universal type converge, in the variational sense, as the sequence length increases. Consequently, the normalized logarithms of the probabilities assigned by any kth order probability assignment to two sequences of the same universal type, as well as the kth order empirical entropies of the sequences, converge for all k. We study the size of a universal type class, and show that its asymptotic behavior parallels that of the conventional counterpart, with the LZ78 code length playing the role of the empirical entropy. We also estimate the number of universal types for sequences of length n, and show that it is of the form exp((1+o(1))γ n/log n) for a well characterized constant γ. We describe algorithms for enumerating the sequences in a universal type class, and for drawing a sequence from the class with uniform probability. As an application, we consider the problem of universal simulation of individual sequences. A sequence drawn with uniform probability from the universal type class of x n is an optimal simulation of x n in a well defined mathematical sense.
(Show Context)Symbolic and parametric model checking of discrete-time markov Chains
'... daws at cs.ru.nl Abstract. We present a language-theoretic approach to symbolic model checking of PCTL over discrete-time Markov chains. The probability with which a path formula is satisfied is represented by a regular expression. A recursive evaluation of the regular expression yields an exact rat ...'
Abstract - Cited by 25 (0 self) - Add to MetaCart daws at cs.ru.nl Abstract. We present a language-theoretic approach to symbolic model checking of PCTL over discrete-time Markov chains. The probability with which a path formula is satisfied is represented by a regular expression. A recursive evaluation of the regular expression yields an exact rational value when transition probabilities are rational, and rational functions when some probabilities are left unspecified as parameters of the system. This allows for parametric model checking by evaluating the regular expression for different parameter values, for instance, to study the influence of a lossy channel in the overall reliability of a randomized protocol. 1
(Show Context)Efficient Approximation of Product Distributions
- in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 1998
'... We describe efficient constructions of small probability spaces that approximate the joint distribution of general random variables. Previous work on efficient constructions concentrate on approximations of the joint distribution for the special case of identical, uniformly distributed random var ...'
Abstract - Cited by 22 (2 self) - Add to MetaCart We describe efficient constructions of small probability spaces that approximate the joint distribution of general random variables. Previous work on efficient constructions concentrate on approximations of the joint distribution for the special case of identical, uniformly distributed random variables. Preliminary version has appeared in the Proceedings of the 24th ACM Symp. on Theory of Computing (STOC), pages 10--16, 1992. y Dept. of Electrical Engineering--Systems, Tel--Aviv University, Ramat--Aviv, Tel--Aviv 69978, Israel. Email: [email protected]. z Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel. Email: [email protected]. Research partially supported by grant No. 89-00312 from the United StatesIsrael Binational Science Foundation (BSF), Jerusalem, Israel. x International Computer Science Institute, Berkeley, CA 94704, USA. Email: [email protected]. Research supported in part by National Science Founda...
Fully Dynamic Secret Sharing Schemes
'... We consider secret sharing schemes in which the dealer is able (after a preprocessing stage) to activate a particular access structure out of a given set and/or to allow the participants to reconstruct different secrets (in different time instants) by sending them the same broadcast message. In this ...'
Abstract - Cited by 19 (1 self) - Add to MetaCart We consider secret sharing schemes in which the dealer is able (after a preprocessing stage) to activate a particular access structure out of a given set and/or to allow the participants to reconstruct different secrets (in different time instants) by sending them the same broadcast message. In this paper we establish a formal setting to study secret sharing schemes of this kind. The security of the schemes presented is unconditional, since they are not based on any computational assumption. We give bounds on the size of the shares held by participants, on the size of the broadcast message, and on the randomness needed in such schemes. 1 Introduction A secret sharing scheme is a method of dividing a secret s among a set P of participants in such a way that: if the participants in A ` P are qualified to know the secret then by pooling together their information they can reconstruct the secret s; but any set A of participants not qualified to know s has absolutely no information on the...
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Abstract: Random numbers play a crucial role in science and industry. Many numericalmethods require the use of random numbers, in particular the Monte Carlomethod. Therefore it is of paramount importance to have efficient random numbergenerators. The differences, advantages and disadvantages of true and pseudorandom number generators are discussed with an emphasis on the intrinsicdetails of modern and fast pseudo random number generators. Furthermore,standard tests to verify the quality of the random numbers produced by a givengenerator are outlined. Finally, standard scientific libraries with built-ingenerators are presented, as well as different approaches to generatenonuniform random numbers. Potential problems that one might encounter whenusing large parallel machines are discussed.
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From: Helmut Katzgraber [view email][v1]Sat, 22 May 2010 10:10:33 UTC (762 KB)
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