Your personal information and card details are 100% secure. Cryptology ePrint Archive: Search Results 2017/635 ( PDF) PERUN: Virtual Payment Channels over Cryptographic Currencies Stefan Dziembowski and Lisa Eckey. This paper gives a review on existing scheduling methodologies developed for process industries.
You might be able to use a, if you're happy with the shape of that distribution. Set n=12 and p=0.25. This will give you a value between 0 and 12 with a mean of 3. Just add 2 to each result to get the range and mean you are looking for.
Edit: As for implementation, you can probably find a library for your chosen language that supports non-uniform distributions (I've ). A binomial distribution can be approximated fairly easily using a uniform RNG. Simply perform n trials and record the number of successes. So if you have n=10 and p=0.5, it's just like flipping a coin 10 times in a row and counting the number of heads. For p=0.25 just generate uniformly-distributed values between 0 and 3 and only count zeros as successes. If you want a more efficient implementation, there is a clever algorithm hidden away in the exercises of volume 2 of Knuth's The Art of Computer Programming.
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.
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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). 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.
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 rate Omega Gammate/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. 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. 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.
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.
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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. 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.