Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graph...
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Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is # P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called lambda-rings network, and focuses on an unreliable lambda-rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the divide-and-conquer approach to design a fast algorithm for computing an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(parallel to lambda parallel to(2)(2) + [log vertical bar lambda vertical bar] center dot parallel to lambda parallel to).
Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graph...
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ISBN:
(纸本)9783642174605
Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called lambda-rings network, and focuses on an unreliable lambda-rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the divide-and-conquer approach to design a fast algorithm for computing its an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(parallel to lambda parallel to(2)(2) + inverted right perpendicularlog vertical bar lambda vertical bar inverted left perpendicular . parallel to lambda parallel to(1))
In addressing the significant influence of material dielectric parameters on outdoor three-dimensional ray tracing predictions, an algorithm based on divide-and-conquer strategy for calibrating the dielectric properti...
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ISBN:
(纸本)9798350353129;9798350353136
In addressing the significant influence of material dielectric parameters on outdoor three-dimensional ray tracing predictions, an algorithm based on divide-and-conquer strategy for calibrating the dielectric properties of materials is proposed. The algorithm segments the solution space for dielectric parameters into smaller sub-spaces, resolving each incrementally to arrive at the global optimal solution. It employs a prudent convergence strategy for the solution space, discarding those sub-spaces that have a low probability of containing the optimum. The results indicate that this algorithm not only maintains high accuracy but also facilitates rapid calibration of dielectric parameters.
Curve fitting is still an open problem which draws attention from many applications, such as computer-aided design, computer-aided manufacturing and reverse engineering. Splines such as Bezier, B-Spline and NURBS curv...
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Curve fitting is still an open problem which draws attention from many applications, such as computer-aided design, computer-aided manufacturing and reverse engineering. Splines such as Bezier, B-Spline and NURBS curves are usually employed in engineering applications and are intensively used for fitting purposes. The optimization of their shapes and localization parameters, however, is a very complex task. The literature presents many methods which empirically set some important parameters, such as the number of control points. As guessing such a value is difficult, this paper presents a new method to choose it through a multi-curve fitting method, based on linear least square optimizations, using a divide-and-conquer algorithm and an error tolerance threshold. Four prime procedures compose the method: the conquer step fits curves over subset point clouds;the combine step glues curve segments together with some selective continuity;the divide step splits subsets which are not properly fitted yet;and the merge step blends curve segments together. Several curve setups were tested in well-known benchmarks, using four-division strategies: bisection, error balance, point with the greatest curvature and point with the smallest curvature. The developed method allows for fast computation even for larger point clouds, and it was able to properly reconstruct each tested shape, even with the addition of synthetic noise. We also demonstrate that it can be significantly faster than a single-curve fitting using the same number of control points.(c) 2022 Elsevier Ltd. All rights reserved.
In this paper, we consider networks with topologies described by some connected undirected graph G = (V, E) and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, an...
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In this paper, we consider networks with topologies described by some connected undirected graph G = (V, E) and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and optimization problem mini {F(i) = n-ary sumation ������is an element of V f ������(i)} with local objective functions f ������ depending only on neighboring variables of the vertex ������ is an element of V. We introduce a divide-and-conquer algorithm to solve the above optimization problem in a distributed and decentralized manner. The proposed divide-and-conquer algorithm has exponential convergence, its computational cost is almost linear with respect to the size of the network, and it can be fully implemented at fusion centers of the network. In addition, our numerical demonstrations indicate that the proposed divide-and-conquer algorithm has superior performance than popular decentralized optimization methods in solving the least squares problem, both with and without the ������1 penalty, and exhibits great performance on networks equipped with asynchronous local peer-to-peer communication.
For rigid multibody systems with redundant constraints, mathematical modeling and physical interpretation of the obtained results are impeded due to the nonuniqueness of the calculated reactions, which-in the case of ...
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For rigid multibody systems with redundant constraints, mathematical modeling and physical interpretation of the obtained results are impeded due to the nonuniqueness of the calculated reactions, which-in the case of load-dependent joint friction-may additionally lead to unrealistic simulated motion. It makes the uniqueness analysis crucial for assessing the fidelity of the results. The developed methods so far for the uniqueness examination-based on the modified mobility equation, the constraint matrix, or the free-body diagram-are not well suited for multibody systems described by relative coordinates. The novel method discussed in this paper breaks this limitation. The proposed approach is based on the divide-and-conquer algorithm (DCA)-a low-order recursive method for dynamic simulations of complex multibody systems. The devised method may be used for checking the joint-reaction uniqueness of holonomic systems with ideal constraints that fulfill some additional assumptions. The reaction-uniqueness analysis is performed when the main pass of the DCA is completed. An eight-step algorithm is proposed. In the case of the single-joint connections, it is sufficient to study the appropriate equations of motion. However, if the multijoint connection is present, then one of the numerical methods-known from the constraint-matrix-based or the free-body-diagram-based approach-has to be used, namely the rank-comparison, QR-decomposition, SVD, or nullspace methods;all of these approaches are discussed. To illustrate the devised method, a spatial parallelogram mechanism with a triple pendulum is analyzed.
The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V (1),V (2),aEuro broken vertical bar,V (k) so that E-i=1(k) f(V-i) is minimized where f is a non-ne...
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The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V (1),V (2),aEuro broken vertical bar,V (k) so that E-i=1(k) f(V-i) is minimized where f is a non-negative submodular function on V. In this paper, we design an approximation algorithm for the problem with fixed k. We also analyze the approximation factor of our algorithm for the hypergraph k-cut problem, which is a problem contained by the submodular system k-partition problem.
The goal of this paper is to describe a rather general approach for constructing upper and lower bounds for the average computational complexity of divide-and-conquer algorithms.
The goal of this paper is to describe a rather general approach for constructing upper and lower bounds for the average computational complexity of divide-and-conquer algorithms.
In this paper, two accelerated divide-and-conquer (ADC) algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost O(N(2)r) flops in the worst case, where N is the dimension of the matrix and...
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In this paper, two accelerated divide-and-conquer (ADC) algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost O(N(2)r) flops in the worst case, where N is the dimension of the matrix and r is a modest number depending on the distribution of eigenvalues. Both of these algorithms use hierarchically semiseparable (HSS) matrices to approximate some intermediate eigenvector matrices, which are Cauchy-like matrices and are off-diagonally low-rank. The difference of these two versions lies in using different HSS construction algorithms, one (denoted by ADC1) uses a structured low-rank approximation method and the other (ADC2) uses a randomized HSS construction algorithm. For the ADC2 algorithm, a method is proposed to estimate the off-diagonal rank. Numerous experiments have been carried out to show their stability and efficiency. These algorithms are implemented in parallel in a shared memory environment, and some parallel implementation details are included. Comparing the ADCs with highly optimized multi-threaded libraries such as Intel MKL, we find that ADCs could be more than six times faster for some large matrices with few deflations. Copyright (C) 2016 John Wiley & Sons, Ltd.
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subs...
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This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank updates of matrix functions. Our convergence analysis of the newly proposed method proceeds by establishing relations to best polynomial and rational approximation. When only the trace or the diagonal of the matrix function is of interest, we demonstrate---in practice and in theory---that convergence can be faster. For the special case of a banded matrix, we show that the divide-and-conquer method reduces to a much simpler algorithm, which proceeds by computing matrix functions of small submatrices. Numerical experiments confirm the effectiveness of the newly developed algorithms for computing large-scale matrix functions from a wide variety of applications.
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