Given a random variable chi which takes n equiprobable values, we consider several algorithmic questions related to the classical problem of simulating the outcomes of chi by using a limited number of biased coins.
Given a random variable chi which takes n equiprobable values, we consider several algorithmic questions related to the classical problem of simulating the outcomes of chi by using a limited number of biased coins.
Identifying what problems can be solved in a given distributed system is a central question in distributed computing. In this series of works, we study this question in the context of asynchronous fault tolerant syste...
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Identifying what problems can be solved in a given distributed system is a central question in distributed computing. In this series of works, we study this question in the context of asynchronous fault tolerant systems that can execute consensus. These systems can be those executing deterministic protocols with access to a consensus routine or those running randomized error-free protocols. A previous work handled the class of distributed decision tasks. In these tasks, each processor receives one local input and has to respond with one local output. In an interactive distributed task each of n processors receives a sequence of local inputs and has to respond on line with an output for every new input (before getting its next input). Different processors can be at different stages concurrently, so that additional inputs are received by fast processors while slow processors are still working on early inputs. An interactive task is called finite if the number of local inputs (and outputs) is finite. Interactive tasks can neither be described as a single huge decision task nor be decomposed into distinct, independent decision tasks. The main result of this work is an exact characterization of the finite interactive tasks which can be solved by t-resilient protocols in either of the above two models. The major tool we use in the characterization is a directed acyclic graph that is associated with an interactive task. Properties of this graph are used to determine the resiliency of the task and to devise a "generic" resilient algorithm which solves such tasks. This generic algorithm can be viewed as a repeated, deterministic reduction to a consensus subroutine. This implies that any finite interactive task is solvable by randomized error-free protocols iff it is solvable by deterministic protocols with access to consensus.
We present real, complex, and quaternionic versions of a simple randomized polynomial time algorithm to approximate the permanent of a nonnegative matrix and, more generally, the mixed discriminant of positive semidef...
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We present real, complex, and quaternionic versions of a simple randomized polynomial time algorithm to approximate the permanent of a nonnegative matrix and, more generally, the mixed discriminant of positive semidefinite matrices. The algorithm provides an unbiased estimator, which, with high probability, approximates the true value within a factor of O(c(n)), where n is the size of the matrix (matrices) and where c approximate to 0.28 for the real version, c approximate to 0.56 for the complex version, and c approximate to 0.76 for the quaternionic version. We discuss possible extensions of our method as well as applications of mixed discriminants to problems of combinatorial counting. (C) 1999 John Wiley & Sons, Inc.
This paper presents a new approach to heat exchanger network (HEN) design making extensive use of randomization techniques. It is exceedingly simple to implement and gives new insight into the hardness and the cost la...
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This paper presents a new approach to heat exchanger network (HEN) design making extensive use of randomization techniques. It is exceedingly simple to implement and gives new insight into the hardness and the cost landscape underlying a given problem. At the same time, the results from our algorithm may be used as good initial solutions required by most non-linear optimization problem formulations of HEN design. Practical networks involve trade-off between a number of factors, all of which are difficult to incorporate in a single design methodology. Our approach is blind to any design heuristic and generates a sufficiently large number of networks that can be further evaluated to pick up the most suitable network depending on specific design requirements. However, the current version of the algorithm is limited to HEN synthesis problems that can be solved without stream splitting. We have experimented with the three standard literature problems and obtained results that compare well with the previously published results, which justify further research in this direction. (C) 1999 Elsevier Science S.A. All rights reserved.
In the edge connectivity augmentation problem one wants to find an edge set of minimum total capacity that increases the edge connectivity of a given undirected graph by tau. It is a known non-trivial property of the ...
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In the edge connectivity augmentation problem one wants to find an edge set of minimum total capacity that increases the edge connectivity of a given undirected graph by tau. It is a known non-trivial property of the edge connectivity augmentation problem that there is a sequence of edge sets E-1, E-2,..., such that boolean OR(i)less than or equal to E-i optmially increases the connectivity by tau, for any integer tau. The main result of the paper is that this sequence of edge sets can be divided into O(n) groups such that within one group, all E-i are basically the same. Using this result, we improve on the running time of edge connectivity augmentation, as well as we give the first parallel (RNC) augmentation algorithm. We also present new efficient subroutines for finding the so-called extreme sets and the cactus representation of min-cuts required in our algorithms. Augmenting the connectivity of hypergraphs with ordinary edges is known to be structurally harder than that of ordinary graphs. In a weaker version when one exceptional hyperedge is allowed in the augmenting edge set, we derive similar results as for ordinary graphs.
We study the geometric properties of point sets that arise in the generation of bounded aspect-ratio meshes and present a constructive formulation to define distributions that allow arbitrary refinements. This formula...
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We study the geometric properties of point sets that arise in the generation of bounded aspect-ratio meshes and present a constructive formulation to define distributions that allow arbitrary refinements. This formulation can be used to define distributions with one or more singularities, which do not occur in the uniform case but do occur in mesh generation for real-world applications. We give an efficient algorithm for the generation of a point set from these distributions. This work is in part motivated by the following observation: The Poisson distribution, points placed uniformly and randomly in a fixed dimension, is one of the most commonly used classes of data sets in the experimental evaluation of geometric algorithms and their implementation. However, despite its importance and interest to computational geometry, the Poisson distribution fails to be good test data for triangulation algorithms and software for mesh generation. Consequently, many implemented sequential and parallel algorithms are tuned to work efficiently for the uniform distribution, but fail to be efficient for nonuniform distributions. Even though the focus of our work is on the generation of data for Delaunay-based mesh algorithms, we hope that it will motivate further theoretical investigations on the generation of data for other geometric algorithms and software.
Consider an unknown function L(.):{1,..., d}-->{1,..., r}with range R = {L(i)\i = 1,..., d}. Given d, r, epsilon, delta > 0 we show how to compute an estimate (p) over tilde such that with probability at least 1...
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Consider an unknown function L(.):{1,..., d}-->{1,..., r}with range R = {L(i)\i = 1,..., d}. Given d, r, epsilon, delta > 0 we show how to compute an estimate (p) over tilde such that with probability at least 1 - delta we have \\R\/r-(p) over tilde\ less than or equal to epsilon (p) over tilde. This is an estimate with a fixed relative error, which is stronger than finding an estimate with a fixed absolute error. This calculation can be performed efficiently in one pass through the domain of L (allowing the the method to be used in online situations) using only O(logr(loglogr + log 1/delta)/epsilon(2)) words of storage. The method is based on pairwise-independent pseudo-random variables. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper we study the probabilistic real stability radius , which gives a description of the degradation of the probability of stability beyond the classical real stability radius. The main result of the paper is...
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In this paper we study the probabilistic real stability radius , which gives a description of the degradation of the probability of stability beyond the classical real stability radius. The main result of the paper is to determine the probability density function of the singular values of the perturbation matrix ▵. Subsequently, we propose an algorithm for uniform generation of matrix samples, so that the probability of stability can be effectively estimated via a randomized algorithm.
We present a randomized algorithm which generalizes ideas of K. L. CLARKSON, R. SEIDEL and E. WELZL for LP to problems with a convex objective function and affine constraints. An analysis of the expected running time ...
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We present a randomized algorithm which generalizes ideas of K. L. CLARKSON, R. SEIDEL and E. WELZL for LP to problems with a convex objective function and affine constraints. An analysis of the expected running time of the main algorithm shows a linear dependency on the number of constraints, but an exponential one on the dimension which can be somewhat improved by applying several modifications. We finally report some numerical results.
The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. in this paper we present efficient algorith...
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The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. in this paper we present efficient algorithms for packet routing, sorting, and selection on the OTIS-Mesh. The diameter of an N-2-processor OTIS-Mesh is 4 root N - 3. We present an algorithm for routing any partial permutation in 4 root N + o(root N) time. Our selection algorithm runs in time 6 root N + o(root N) and our sorting algorithm runs in 8 root N + o(root N) time. All these algorithms are randomized and the stated time bounds hold with high probability. Also, the queue size needed for these algorithms is O(1) with high probability.
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