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TOTALLY PARALLEL MULTILEVEL ALGORITHMS

1989
*
International journal of high speed computing
*

In fact, all four can be formulated as particular cases of the same

doi:10.1142/s0129053389000123
fatcat:62ianmje2vc2dk5d7ygwgxzz5u
*totally**parallel**multilevel**algorithm*, which we will refer to as TPMA. ... In fact, all four can be formulated as particular cases of the same*totally**parallel**multilevel**algorithm*, which we will refer to as TPMA. ... We describe the general*algorithm*TPMA (*Totally**Parallel**Multilevel**Algorithm*) in section three, after establishing some notation in section two. ...##
###
Mesh Partitioning Algorithm Based on Parallel Finite Element Analysis and Its Actualization

2013
*
Mathematical Problems in Engineering
*

So that it can reduce the application of the threshold of graph partitioning

doi:10.1155/2013/751030
fatcat:57pnxoy7s5ealeace3pxj64bfq
*algorithm*, improve the calculation efficiency, and promote the application of graph theory and*parallel*computing. ... In*parallel*computing based on finite element analysis, domain decomposition is a key technique for its preprocessing. ... The*algorithm*actualized in ParMetis is based on*parallel**multilevel*K-path partitioning method, self-adaptive repartitioning*algorithm*, and*parallel*multiconstraint*algorithm*. ...##
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Engineering Graph Partitioning Algorithms
[chapter]

2012
*
Lecture Notes in Computer Science
*

required

doi:10.1007/978-3-642-30850-5_3
fatcat:zkee6zsjcjbv7iaxrmjdkocrx4
*total*node weight of each block ≤ 1 + k*total*node weight*total*weight of cut edges as small as possible Applications: various numerical simulations, VLSI design, route planning, . . . ... Simulation space is discretized into a mesh Solution of partial differential equations are approximated by linear equations Number of vertices can become quite large → time and memory*Parallel*processing ... + + + Introduction*Multilevel**Algorithms*Coarsening Initial Partitioning Local Improvement Intelligently using multiple runs*Parallelization*Experiments Discussion Iterated*Multilevel*[Walshaw ...##
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Scalable Parallel Algorithms for Sparse Linear Systems
[chapter]

1997
*
Applied Optimization
*

We have recently developed a

doi:10.1007/978-1-4613-3400-2_4
fatcat:ceqkeglhnjexxex4chrt4gldrm
*parallel*formulation of the*multilevel*graph partitioning*algorithm*. ... Even though these*multilevel**algorithms*are quite fast compared with spectral methods, performing a*multilevel*partitioning in*parallel*is desirable for the following reasons. ...##
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Serial and Parallel Multilevel Graph Partitioning Using Fixed Centers
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present new serial and

doi:10.1007/978-3-540-30577-4_16
fatcat:clcjvw2ugjfsnnt77yjaon7nii
*parallel**algorithms*for*multilevel*graph partitioning. Our*algorithm*has coarsening, partitioning and uncoarsening phases like other*multilevel*partitioning methods. ... Using this*algorithm*, it is possible to obtain theoretically and experimentally much more balanced partitions with substantially decreased*total*edge costs between the partitions than other*algorithms*. ... In this study, we propose new serial and*parallel**multilevel**algorithms*for graph partitioning. We compare these methods with the*multilevel*graph partitioning method of [10] . ...##
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Multilevel Diffusion Schemes for Repartitioning of Adaptive Meshes

1997
*
Journal of Parallel and Distributed Computing
*

In this paper, we present schemes for computing repartitionings of adaptively refined meshes that perform diffusion of vertices in a

doi:10.1006/jpdc.1997.1410
fatcat:x3e4pha4ufc23obhsokrfkkbye
*multilevel*framework. ... We also show that*multilevel*diffusion produces results with improved edge-cuts over single-level diffusion, and is better able to make use of heuristics to control the tradeoff between edge-cut and vertex ...*PARALLEL*FORMULATION OF*MULTILEVEL*DIFFUSION We have implemented the*multilevel*diffusion*algorithms*in PARMETIS, which contains a*parallel*formulation of our*multilevel*k-way graph partitioning*algorithm*...##
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Space and time efficient implementations of parallel nested dissection

1992
*
Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92
*

*Parallel*nested dissection (PND)

*algorithms*, which perform this variable elimination in

*parallel*, have been developed for the PRAM model and for grid architectures. ... performed by PND

*algorithms*. ... The

*total*work performed in

*multilevel*K j is bounded by the work necessary to eliminate all the separator vertices in the

*multilevel*, multiplied by the number of subgraphs in the

*multilevel*. ...

##
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FDPrior: A force-directed based parallel partitioning algorithm for three dimensional integrated circuits on GPGPU

2011
*
Proceedings of 2011 International Symposium on VLSI Design, Automation and Test
*

In recent years, the

doi:10.1109/vdat.2011.5783580
fatcat:uotrz3tyybbyxmtsagov6ntdmm
*multilevel*hypergraph partitioning*algorithms*could earn better performances than non-*multilevel*methods. ... Exploiting the*algorithmic**parallelism*on multi-core architectures becomes the key to attain scalable runtime. ... In the partitioning filed,*multilevel*of FM*algorithm*is a celebrated*algorithm*[33] . Hence, we organize the*multilevel*structure of PP3D as the*multilevel*topology of traditional*algorithm*. ...##
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Parallel multilevel algorithms for hypergraph partitioning

2008
*
Journal of Parallel and Distributed Computing
*

In this paper, we present

doi:10.1016/j.jpdc.2007.11.002
fatcat:6dmfuvcw6ffd3ki6yca6lg6wla
*parallel**multilevel**algorithms*for the hypergraph partitioning problem. ... Finally, we evaluate the impact of introducing*parallel*multi-phase refinement into our*parallel**multilevel**algorithm*in terms of the trade off between improved partition quality and higher runtime cost ...*Parallel**Multilevel*Partitioning*Algorithm*This section describes our*parallel*hypergraph partitioning*algorithm*, based on the*multilevel*paradigm. ...##
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Parallel numerical algorithms for optimization of electrical cables

2008
*
Mathematical Modelling and Analysis
*

*Parallel*

*multilevel*

*algorithms*are developed using the master-slave and data decomposition paradigms [4] . ... Results of computational experiments are presented and the efficiency of the proposed

*parallel*

*algorithms*is investigated. ...

*Parallel*

*multilevel*

*algorithms*are developed using the master-slave and data decomposition paradigms [4] . ...

##
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Distributed block independent set algorithms and parallel multilevel ILU preconditioners

2005
*
Journal of Parallel and Distributed Computing
*

Numerical experiments indicate that our domain-based

doi:10.1016/j.jpdc.2004.10.007
fatcat:blirdwg2jbdkljz2ly6akgjl3u
*parallel**multilevel*block ILU preconditioners are robust and efficient. ... We present a class of*parallel*preconditioning strategies utilizing*multilevel*block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. ... One of the most important steps in*parallel**multilevel*block ILU preconditioning techniques is to develop*algorithms*for constructing BIS efficiently from a distributed sparse matrix. ...##
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A multilevel parallel solver for block tridiagonal and banded linear systems

1990
*
Parallel Computing
*

, processor allocation and communication for the

doi:10.1016/0167-8191(90)90029-9
fatcat:br4wmallv5exhmrdcc5ghzycta
*multilevel**algorithm*. ... Acknowledgement The careful implementation of the*multilevel**algorithms*together with the numerical ex periments were done by Per Ulkjaer Andersen who also contributed to the principles behind load balancing ... The solution*algorithm*examplified by Fig. 5.2 is applied to a*multilevel*LU-factorization produced by the*parallel**multilevel*LU-factorization*algorithm*. ...##
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Parallel multilevel k-way partitioning scheme for irregular graphs

1996
*
Proceedings of the 1996 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '96
*

In this paper we present a

doi:10.1145/369028.369103
fatcat:fs6spatx6vbcpcvsg5jibkl3my
*parallel*formulation of a*multilevel*k-way graph partitioning*algorithm*. ... Furthermore, the quality of the partitions produced is comparable (edge-cuts within 5%) to those produced by the serial*multilevel*k-way*algorithm*. ... Section 2 briefly describes the serial*multilevel*k-way partitioning*algorithm*. Section 4 details our*parallel*formulation of the*multilevel*k-way partitioning*algorithm*. ...##
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Partitioning sparse rectangular matrices for parallel computations of Ax and A T v
[chapter]

1998
*
Lecture Notes in Computer Science
*

We then describe how to use (modied)

doi:10.1007/bfb0095342
fatcat:ffogysqqozh6lf372h4vltinuq
*multilevel*methods to partition these graphs and how to implement the matrix multiplies in*parallel*to take advantage of the partitioning. ... Finally, we compare various*multilevel*and other partitioning strategies on matrices from dierent applications. The*multilevel*methods are shown to be best. ... Introduction In many*parallel**algorithms*, we require numerous matrix-vector and matrixtranspose-vector multiplies with sparse matrices. ...##
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Effective cross-platform, multilevel parallelism via dynamic adaptive execution

2002
*
Proceedings 16th International Parallel and Distributed Processing Symposium
*

This

doi:10.1109/ipdps.2002.1016495
dblp:conf/ipps/KoYNP02
fatcat:ge65dyzbvbhzxdt6dhvbagls4a
*algorithm*can be used as a rule of thumb for automatic*multilevel**parallelization*. The effectiveness of the approach is demonstrated on the NAS benchmarks running on two architectural platforms. ... This paper presents preliminary efforts to develop compilation and execution environments that achieve performance portability of*multilevel**parallelization*on hierarchical architectures. ... The*algorithm*is executed at runtime, working its way from single-level*parallelization*to two-level*parallelization*, three-level*parallelization*and so on. ...
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