Distributed QR Factorization Based on Randomized Algorithms

Straková, Hana; Gansterer, Wilfried N.; Zemen, Thomas

doi:10.1007/978-3-642-31464-3_24

Cited by 24 publications

(20 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, in aggregation-based distributed matrix operations (see [15,16]), complex phenomena have to be expected due to the complexity of the algorithms and the potentially large number of distributed aggregation processes involved. Moreover, we work on a fine-grained ns-3 [17]-based simulation environment which allows for simulating aspects which are out of reach of the current theoretical results available for the discussed algorithms.…”

Section: Discussionmentioning

confidence: 99%

Robust Gossip-Based Aggregation: A Practical Point of View

Niederbrucker

Gansterer

2013

2013 Proceedings of the Fifteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

View full text Add to dashboard Cite

Over the last years, several gossip-based aggregation algorithms have been developed which focus on providing resilience in failure-prone distributed systems. The main objective of such algorithms is the efficient in-network computation of aggregates even in the case when system failures occur during runtime. In this paper, we evaluate performance and limitations in practical computations of those gossip-based aggregation algorithms with the most promising theoretical fault tolerance properties.Theoretical analyses of these algorithms usually address only the principal ability of handling or overcoming a certain kind of system failure. Most of the time, there are no formal results on the concrete impact of failure handling on the performance of the algorithms, e. g., in terms of convergence speed. This leaves a wide gap between theory and practice, as we illustrate in this paper. In order to bridge this gap, we first categorize common system failures of interest. Then, we experimentally investigate how well these common failure types are handled in practice by the considered algorithms and up to which extent these state-of-the-art methods provide a reasonable degree of fault tolerance in practice. Our experimental studies reveal (i) that certain failure handling approaches which work in theory exhibit unacceptable performance in practice and (ii) that in some cases the failure handling mechanisms used introduce new problems, e. g., numerical inaccuracy.Our investigations illustrate that for some failure types (such as permanent node failures) further algorithmic advances are required to achieve resilience with a reasonably small overhead and acceptable performance.

show abstract

Section: Discussionmentioning

confidence: 99%

Robust Gossip-Based Aggregation: A Practical Point of View

Niederbrucker

Gansterer

2013

2013 Proceedings of the Fifteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Specifically, in [4] authors used distributed CGS based on gossiping for solving a distributed LS problem and in [5] a gossip-based distributed algorithm for modified Gram-Schmidt orthogonalization (MGS) was designed and analyzed. A slight modification of the latter algorithm was introduced in [9], which we use for comparison in this paper.…”

Section: B Existing Distributed Methodsmentioning

confidence: 99%

“…We focus on standard algorithms for distributed QR factorization based on the GramSchmidt orthogonalization [1], a method which besides computing an orthonormal matrix obtains also an upper triangular matrix containing the set of projection coefficients. In contrast to parallel QR factorization algorithms (e.g., [2], [3]), distributed QR factorization algorithms designed for loosely coupled distributed systems with independently operating nodes and with possibly unreliable communication links have hardly been investigated [4], [5]. In the signal processing area, QR factorization is used widely in many applications, mostly involving linear least squares (LS) problems [4], [6].…”

mentioning

confidence: 98%

Distributed Gram-Schmidt orthogonalization based on dynamic consensus

Slučiak¹,

Straková

Rupp³

et al. 2012

2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)

Self Cite

View full text Add to dashboard Cite

We propose a novel distributed QR factorization algorithm for orthogonalizing a set of vectors in a wireless sensor network. The algorithm originates from the classical GramSchmidt orthogonalization which we formulate in a distributed way using the dynamic consensus algorithm. In contrast to existing distributed QR factorization algorithms, all elements of matrices Q and R are computed simultaneously and updated iteratively after each transmission. Assuming synchronous message broadcasting and communication only with neighboring nodes without any central computing unit (fusion center), we prove convergence of the algorithm. We investigate the algorithm in terms of numerical accuracy and we discuss the influence of the initial data distribution on the algorithm performance. Moreover, we provide a comparison with existing distributed QR algorithms in terms of communication cost and memory requirements, and we illustrate the comparison by simulations.Index Terms-distributed algorithms, Gram-Schmidt orthogonalization, QR factorization, dynamic consensus algorithm, wireless sensor network.

show abstract

“…This least square solver first computes the local solution using distributed QR, which in turn uses gossip-based distributed modified GramSchmidt method described in [29]. This method uses distributed matrix-vector multiplication that can be expensive for a large sparse matrix.…”

Section: Related Workmentioning

confidence: 99%

“…Some of the features that makes gossip methods attractive are: i) absence of central entity or coordinator node ii) high fault tolerance and robustness iii) self healing or error recovery mechanism [31] iv) efficient message exchange due to only neighbor communication v) provision for asynchronous communication. These interesting characteristics make them suitable for WSN to carry out decentralized computation [29].…”

Section: Distributed Randomized Kaczmarzmentioning

confidence: 99%

Distributed Randomized Kaczmarz and Applications to Seismic Imaging in Sensor Network

Kamath

Ramanan

Song

2015

2015 International Conference on Distributed Computing in Sensor Systems

View full text Add to dashboard Cite

Many real-world wireless sensor network applications such as environmental monitoring, structural health monitoring, and smart grid can be formulated as a leastsquares problem. In distributed Cyber-Physical System (CPS), each sensor node observes partial phenomena due to spatial and temporal restriction and is able to form only partial rows of leastsquares. Traditionally, these partial measurements were gathered at a centralized location. However, with the increase in sensors and their measurements, aggregation is becoming challenging and infeasible. In this paper, we propose distributed randomized kaczmarz that performs in-network computation to solve leastsquares over the network by avoiding costly communication. As a case study, we present a volcano monitoring application on a distributed CORE emulator and use real data from Mt. St. Helens to evaluate our proposed method.

show abstract

Distributed QR Factorization Based on Randomized Algorithms

Cited by 24 publications

References 11 publications

Robust Gossip-Based Aggregation: A Practical Point of View

Robust Gossip-Based Aggregation: A Practical Point of View

Distributed Gram-Schmidt orthogonalization based on dynamic consensus

Distributed Randomized Kaczmarz and Applications to Seismic Imaging in Sensor Network

Contact Info

Product

Resources

About