This paper studies the fault detection problem in ship propulsion systems based on randomized algorithms. The nominal propulsion system model, model with uncertainties and model with additive and multiplicative faults...
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This paper studies the fault detection problem in ship propulsion systems based on randomized algorithms. The nominal propulsion system model, model with uncertainties and model with additive and multiplicative faults are first addressed in the form of normalized left coprime factorization (LCF), respectively. The -gap metric is then introduced to measure how far the system deviates from the nominal operation. To reduce the conservatism in the norm-based threshold, a threshold setting law and the estimation of fault detection rate (FDR) are formulated on the probabilistic assumption of uncertain and faulty parameters. The simulation results on the ship propulsion system show that the randomized technique is an efficient solution to deal with the fault detection issues.
randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wi...
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randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices that are not themselves rank-deficient but have off-diagonal blocks that are;specifically, the class of so-called hierarchically semiseparable (HSS) matrices. HSS matrices arise frequently in numerical analysis and signal processing, particularly in the construction of fast methods for solving differential and integral equations numerically. The HSS structure admits algebraic operations (matrix-vector multiplications, matrix factorizations, matrix inversion, etc.) to be performed very rapidly, but only once the HSS representation of the matrix has been constructed. How to rapidly compute this representation in the first place is much less well understood. The present paper demonstrates that if an N x N matrix can be applied to a vector in O(N) time, and if individual entries of the matrix can be computed rapidly, then provided that an HSS representation of the matrix exists, it can be constructed in O(N k(2)) operations, where k is an upper bound for the numerical rank of the off-diagonal blocks. The point is that when legacy codes (based on, e. g., the fast multipole method) can be used for the fast matrix-vector multiply, the proposed algorithm can be used to obtain the HSS representation of the matrix, and then well-established techniques for HSS matrices can be used to invert or factor the matrix.
A randomized algorithm with stream splitting for design of heat exchanger networks is presented in this work. The algorithm has provisions for splitting any one of the process streams. We have studied three benchmark ...
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A randomized algorithm with stream splitting for design of heat exchanger networks is presented in this work. The algorithm has provisions for splitting any one of the process streams. We have studied three benchmark problems taken from literature. The results obtained from these studies clearly indicate the strength of the randomization method in finding a cost-effective network. This random search method can find better networks, which are sometimes unnoticed by other optimization techniques. The simplicity of this method as well as the networks obtained is an additional attractive feature, which should encourage the designers to use it. From the results of this study, randomization is recommended as a reliable check for designing heat exchanger networks. (c) 2006 Elsevier Ltd. All rights reserved.
Two-dimensional strip packing problem is to pack given rectangular pieces on a strip of stock sheet having fixed width and infinite height. Its aim is to minimize the height of the strip such that non-guillotinable an...
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Two-dimensional strip packing problem is to pack given rectangular pieces on a strip of stock sheet having fixed width and infinite height. Its aim is to minimize the height of the strip such that non-guillotinable and fix orientation constraints are meet. In this paper, an improved scoring rule is developed and the least waste priority strategy is introduced, and a randomized algorithm is presented for solving this problem. This algorithm is very simple and does not need to set any parameters. Computational results on a wide range of benchmark problem instances show that the proposed algorithm obtains a better or matching performance as compared to the most of the previously published meta-heuristics. (C) 2012 Elsevier Ltd. All rights reserved.
We describe a randomized algorithm for assigning neighbours to vertices joining a dynamic distributed network. The aim of the algorithm is to maintain connectivity, low diameter and constant vertex degree. On joining ...
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We describe a randomized algorithm for assigning neighbours to vertices joining a dynamic distributed network. The aim of the algorithm is to maintain connectivity, low diameter and constant vertex degree. On joining each vertex donates a constant number of tokens to the network. These tokens contain the address of the donor vertex. The tokens make independent random walks in the network. A token can be used by any vertex it is visiting to establish a connection to the donor vertex. This allows joining vertices to be allocated a random set of neighbours although the overall vertex membership of the network is unknown. The network we obtain in this way is robust under adversarial deletion of vertices and edges and actively reconnects itself. One model we consider is a network constructed in this fashion, in which vertices join but never leave. If t is the size of the network, then the diameter of the network is O(log t) for all t, with high probability. As an example of the robustness of this model, suppose an adversary deletes edges from the network leaving components of size at least t(1/2+delta). With high probability the network reconnects itself by replacing lost edges using tokens from the token pool. (c) 2008 Elsevier B.V. All rights reserved.
This note is a report of testing a straightforward generalization of the randomized 3-coloring algorithm of Petford and Welsh (1989) on the decision problems of 4- and 10-coloring. We observe similar behavior, namely ...
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This note is a report of testing a straightforward generalization of the randomized 3-coloring algorithm of Petford and Welsh (1989) on the decision problems of 4- and 10-coloring. We observe similar behavior, namely the existence of critical regions. Experimentally, the average time complexity for large n again seems to grow slowly, although in some cases the number of transitions needed is prohibitively high for practical applications.
This paper deals with the min-max version of the problem of selecting p items of the minimum total weight out of a set of n items, where the item weights are uncertain. The discrete scenario representation of uncertai...
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This paper deals with the min-max version of the problem of selecting p items of the minimum total weight out of a set of n items, where the item weights are uncertain. The discrete scenario representation of uncertainty is considered. The Computational complexity of the problem is explored. A randomized algorithm for the problem is then proposed, which returns an O(ln K)-approximate Solution with a high probability, where K is the number of scenarios. This is the first approximation algorithm with better than K worst case ratio for the class of min-max combinatorial optimization problems with unbounded scenario set.
A randomized extension-rotation algorithm is presented to partition an undirected graph G=(V,E) into vertex disjoint paths of fixed length. In O(Absolute value of V log Absolute value of V) time it finds such a partit...
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A randomized extension-rotation algorithm is presented to partition an undirected graph G=(V,E) into vertex disjoint paths of fixed length. In O(Absolute value of V log Absolute value of V) time it finds such a partition if one exists with high probability, when applied to random graphs with sufficiently high edge density.
A randomized algorithm is substantiated for the strongly NP-hard problem of partitioning a finite set of vectors of Euclidean space into two clusters of given sizes according to the minimum-of-the sum-of-squared-dista...
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A randomized algorithm is substantiated for the strongly NP-hard problem of partitioning a finite set of vectors of Euclidean space into two clusters of given sizes according to the minimum-of-the sum-of-squared-distances criterion. It is assumed that the centroid of one of the clusters is to be optimized and is determined as the mean value over all vectors in this cluster. The centroid of the other cluster is fixed at the origin. For an established parameter value, the algorithm finds an approximate solution of the problem in time that is linear in the space dimension and the input size of the problem for given values of the relative error and failure probability. The conditions are established under which the algorithm is asymptotically exact and runs in time that is linear in the space dimension and quadratic in the input size of the problem.
We consider a strongly NP-hard problem of partitioning a finite Euclidean sequence into two clusters of given cardinalities minimizing the sum over both clusters of intracluster sums of squared distances from clusters...
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We consider a strongly NP-hard problem of partitioning a finite Euclidean sequence into two clusters of given cardinalities minimizing the sum over both clusters of intracluster sums of squared distances from clusters elements to their centers. The center of one cluster is unknown and is defined as the mean value of all points in the cluster. The center of the other cluster is the origin. Additionally, the difference between the indices of two consequent points from the first cluster is bounded from below and above by some constants. A randomized algorithm that finds an approximation solution of the problem in polynomial time for given values of the relative error and failure probability and for an established parameter value is proposed. The conditions are established under which the algorithm is polynomial and asymptotically exact.
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