A load balancing parallel algorithm for solving large-scale tridiagonal linear systems

Abstract We present PeerFlow, a system to securely load balance client traffic in Tor. Security in Tor requires that no adversary handle too much traffic. However, Tor relays are run by volunteers who cannot be trusted to report the relay bandwidths, which Tor clients use for load balancing. We show that existing methods to determine the bandwidths of Tor relays allow an adversary with little bandwidth to attack large amounts of client traffic. These methods include Tor’s current bandwidth-scanning system, TorFlow, and the peer-measurement system EigenSpeed. We present an improved design called PeerFlow that uses a peer-measurement process both to limit an adversary’s ability to increase his measured bandwidth and to improve accuracy. We show our system to be secure, fast, and efficient. We implement PeerFlow in Tor and demonstrate its speed and accuracy in large-scale network simulations.

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A new parallel algorithm for solving sparse linear systems

Proceedings of ISCAS'95 - International Symposium on Circuits and Systems ◽

10.1109/iscas.1995.520413 ◽

2002 ◽

Author(s):

K.N. Balasubramanya Murthy ◽

C. Siva Ram Murthy

Keyword(s):

Parallel Algorithm ◽

Linear Systems ◽

Sparse Linear Systems

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A Parallel Algorithm for Solving a Kind of Special Structured Linear Systems

2010 Ninth International Symposium on Distributed Computing and Applications to Business, Engineering and Science ◽

10.1109/dcabes.2010.10 ◽

2010 ◽

Author(s):

Yan Zhong ◽

Zhi-Gang Luo ◽

Feng Wu

Keyword(s):

Parallel Algorithm ◽

Linear Systems

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A fast methodology for large-scale focusing inversion of gravity and magnetic data using the structured model matrix and the 2-D fast Fourier transform

Geophysical Journal International ◽

10.1093/gji/ggaa372 ◽

2020 ◽

Vol 223 (2) ◽

pp. 1378-1397

Author(s):

Rosemary A Renaut ◽

Jarom D Hogue ◽

Saeed Vatankhah ◽

Shuang Liu

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Linear Systems ◽

Large Scale ◽

Surface Measurement ◽

Magnetic Data ◽

Uniform Grid ◽

Data Sets ◽

Inversion Algorithm ◽

Data Set

SUMMARY We discuss the focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid. For the uniform grid, the model sensitivity matrices have a block Toeplitz Toeplitz block structure for each block of columns related to a fixed depth layer of the subsurface. Then, all forward operations with the sensitivity matrix, or its transpose, are performed using the 2-D fast Fourier transform. Simulations are provided to show that the implementation of the focusing inversion algorithm using the fast Fourier transform is efficient, and that the algorithm can be realized on standard desktop computers with sufficient memory for storage of volumes up to size n ≈ 106. The linear systems of equations arising in the focusing inversion algorithm are solved using either Golub–Kahan bidiagonalization or randomized singular value decomposition algorithms. These two algorithms are contrasted for their efficiency when used to solve large-scale problems with respect to the sizes of the projected subspaces adopted for the solutions of the linear systems. The results confirm earlier studies that the randomized algorithms are to be preferred for the inversion of gravity data, and for data sets of size m it is sufficient to use projected spaces of size approximately m/8. For the inversion of magnetic data sets, we show that it is more efficient to use the Golub–Kahan bidiagonalization, and that it is again sufficient to use projected spaces of size approximately m/8. Simulations support the presented conclusions and are verified for the inversion of a magnetic data set obtained over the Wuskwatim Lake region in Manitoba, Canada.

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