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View all- van der Hoeven JMaza MZhi L(2022)On the Complexity of Symbolic ComputationProceedings of the 2022 International Symposium on Symbolic and Algebraic Computation10.1145/3476446.3535493(3-12)Online publication date: 4-Jul-2022
Design and Implementation of Multi-Threaded Algorithms in Polynomial Algebra
Pages 15 - 20
References
[1]
Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company.
[2]
M. Asadi, A. Brandt, C. Chen, S. Covanov, F. Mansouri, D. Mohajerani, R. H. C. Moir, M. Moreno Maza, D. Talaashrafi, Linxiao Wang, Ning Xie, and Yuzhen Xie. 2021. Basic Polynomial Algebra Subprograms (BPAS). www.bpaslib.org.
[3]
Mohammadali Asadi, Alexander Brandt, Robert H. C. Moir, and Marc Moreno Maza. 2019. Algorithms and Data Structures for Sparse Polynomial Arithmetic. Mathematics 7, 5 (2019), 441.
[4]
Mohammadali Asadi, Alexander Brandt, Robert H. C. Moir, Marc Moreno Maza, and Yuzhen Xie. 2021. Parallelization of Triangular Decompositions: Techniques and Implementation. J. Symb. Comput. (2021). (to appear).
[5]
Giuseppe Attardi and Carlo Traverso. 1996. Strategy-Accurate Parallel Buchberger Algorithms. J. Symbolic Computation 22 (1996), 1--15.
[6]
Cédric Bastoul. 2004. Code Generation in the Polyhedral Model Is Easier Than You Think. In Proceedings of the 13th International Conference on Parallel Architectures and Compilation Techniques (PACT '04). IEEE Computer Society, 7--16.
[7]
Laszlo A. Belady. 1966. A Study of replacement algorithms for virtual storage computers. IBM Systems Journal, 5:78--101 (1966).
[8]
Mordechai Ben-Ari. 1990. Principles of concurrent and distributed programming. Prentice Hall.
[9]
Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B Shah. 2017. Julia: A fresh approach to numerical computing. SIAM review 59, 1 (2017), 65--98.
[10]
François Boulier. 1994. Étude et implantation de quelques algorithmes en algèbre différentielle. (Study and implementation of some algorithms in differential algebra). Ph.D. Dissertation. Lille University of Science and Technology, France.
[11]
Russell J. Bradford. 1990. A parallelization of the Buchberger algorithm. In International Symposium on Symbolic and Algebraic Computation (ISSAC '90). ACM, 296.
[12]
Alexander Brandt. 2018. High Performance Sparse Multivariate Polynomials: Fundamental Data Structures and Algorithms. Master's thesis. Western University.
[13]
Alexander Brandt and Marc Moreno Maza. 2021. On the Complexity and Parallel Implementation of Hensel's Lemma and Weierstrass Preparation. In Computer Algebra in Scientific Computing (CASC '21). (submitted).
[14]
Bruno Buchberger. 1987. The parallelization of critical-pair/completion procedures on the L-Machine. In Proceedings of the Japanese Symposium on functional programming. 54--61.
[15]
Changbo Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno Maza, Ning Xie, and Yuzhen Xie. 2016. Parallel Integer Polynomial Multiplication. In 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2016, Timisoara, Romania, September 24-27, 2016. 72--80.
[16]
Changbo Chen and Marc Moreno Maza. 2016. Quantifier elimination by cylindrical algebraic decomposition based on regular chains. J. Symb. Comput. 75 (2016), 74--93.
[17]
Changbo Chen and Marc Moreno Maza. 2012. Algorithms for computing triangular decomposition of polynomial systems. J. Symb. Comput. 47, 6 (2012), 610--642.
[18]
Changbo Chen, Marc Moreno Maza, and Yuzhen Xie. 2011. Cache Complexity and Multicore Implementation for Univariate Real Root Isolation. J. of Physics: Conference Series 341 (2011), 12.
[19]
Muhammad F. I. Chowdhury, Marc Moreno Maza, Wei Pan, and Éric Schost. 2011. Complexity and Performance Results for non FFT-based Univariate Polynomial Multiplication. In Proceedings of Advances in mathematical and computational methods: addressing modern of science, technology, and society, AIP conference proceedings (volume 1368). 259--262.
[20]
Svyatoslav Covanov, Davood Mohajerani, Marc Moreno Maza, and Lin-Xiao Wang. 2019. Big Prime Field FFT on Multi-core Processors. In International Symposium on Symbolic and Algebraic Computation (ISSAC '19), Beijing, China, July 15-18, 2019. 106--113.
[21]
Jean Della Dora and John Fitch (Eds.). 1988. Computer Algebra and Parallelism, First International Workshop, Grenoble, France, September 1989. Academic Press.
[22]
Jean-Guillaume Dumas, Erich L. Kaltofen, and Clément Pernet (Eds.). 2015. Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, PASCO 2015, Bath, United Kingdom, July 10-12, 2015. ACM.
[23]
Howard Whitley Eves. 1980. Elementary matrix theory. Courier Corporation.
[24]
Stijn Eyerman, James E. Smith, and Lieven Eeckhout. 2006. Characterizing the branch misprediction penalty. In 2006 IEEE International Symposium on Performance Analysis of Systems and Software, ISPASS 2006, March 19-21, 2006, Austin, Texas, USA, Proceedings. IEEE Computer Society, 48--58.
[25]
Jean-Charles Faugère and Sylvain Lachartre. 2010. Parallel Gaussian elimination for Gröbner bases computations in finite fields. In Proceedings of the 4th International Workshop on Parallel Symbolic Computation. ACM, 89--97.
[26]
Jean-Charles Faugère, Michael B. Monagan, and Hans-Wolfgang Loidl (Eds.). 2017. Proceedings of the 2017 International Workshop on Parallel Symbolic Computation, PASCO 2017, Kaiserslautern, Germany, July 23-24, 2017. ACM.
[27]
Matteo Frigo, Charles E. Leiserson, Harald Prokop, and Sridhar Ramachandran. 2012. Cache-Oblivious Algorithms. ACM Transactions on Algorithms 8, 1 (2012).
[28]
Matteo Frigo and Volker Strumpen. 2006. The cache complexity of multithreaded cache oblivious algorithms. In Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2006. ACM, 271--280.
[29]
Mickaël Gastineau and Jacques Laskar. 2013. Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-Core Systems. In Computer Algebra in Scientific Computing (CASC '13) (LNCS), Vol. 8136. Springer, 100--115.
[30]
Mickaël Gastineau and Jacques Laskar. 2015. Parallel sparse multivariate polynomial division. In Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, PASCO 2015. ACM, 25--33.
[31]
Armin Größlinger, Martin Griebl, and Christian Lengauer. 2006. Quantifier elimination in automatic loop parallelization. J. Symb. Comput. 41, 11 (2006), 1206--1221.
[32]
Sardar Anisul Haque, Marc Moreno Maza, and Ning Xie. 2014. A Many-core Machine Model for Designing Algorithms with Minimum Parallelism Overheads. CoRR abs/1402.0264 (2014). arXiv:1402.0264 http://arxiv.org/abs/1402.0264
[33]
Sardar Anisul Haque, Marc Moreno Maza, and Ning Xie. 2015. A Many-Core Machine Model for Designing Algorithms with Minimum Parallelism Overheads. In Parallel Computing: On the Road to Exascale, Proceedings of the International Conference on Parallel Computing, ParCo 2015, 1-4 September 2015, Edinburgh, Scotland, UK (Advances in Parallel Computing), Vol. 27. IOS Press, 35--44.
[34]
John L. Hennessy and David A. Patterson. 2012. Computer Architecture - A Quantitative Approach, 5th Edition. Morgan Kaufmann.
[35]
Karin Högstedt, Larry Carter, and Jeanne Ferrante. 1997. Determining the idle time of a tiling. In Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (POPL '97). ACM, 160--173.
[36]
Hoon Hong (Ed.). 1994. Proceedings of the 1st International Workshop on Parallel Symbolic Computation, PASCO 1994, Linz, Austria. World scientific.
[37]
Hoon Hong, Erich Kaltofen, and Markus A. Hitz (Eds.). 1997. Proceedings of the 2nd International Workshop on Parallel Symbolic Computation, PASCO 1997, July 20--22, 1997, Kihei, Hawaii, USA. ACM.
[38]
Sunpyo Hong and Hyesoon Kim. 2009. An analytical model for a GPU architecture with memory-level and thread-level parallelism awareness. In ISCA 2009. 152--163.
[39]
Monica S. Lam, Edward E. Rothberg, and Michael E. Wolf. 1991. The Cache Performance and Optimizations of Blocked Algorithms. In ASPLOS-IV Proceedings. ACM Press, 63--74.
[40]
Charles E. Leiserson. 2011. Cilk. In Encyclopedia of Parallel Computing. 273--288.
[41]
Lin Ma, Kunal Agrawal, and Roger D. Chamberlain. 2014. A memory access model for highly-threaded many-core architectures. Future Generation Comp. Syst. 30 (2014), 202--215.
[42]
Marc Moreno Maza and Yuzhen Xie. 2009. FFT-Based Dense Polynomial Arithmetic on Multi-cores. In High Performance Computing Systems and Applications, 23rd International Symposium, HPCS 2009 (LNCS), Vol. 5976. Springer, 378--399.
[43]
Michael McCool, James Reinders, and Arch Robison. 2012. Structured parallel programming: patterns for efficient computation. Elsevier.
[44]
Michael B. Monagan and Roman Pearce. 2009. Parallel sparse polynomial multiplication using heaps. In International Symposium on Symbolic and Algebraic Computation, (ISSAC '09), Seoul, Republic of Korea, July 29-31, 2009. ACM.
[45]
Michael B. Monagan and Roman Pearce. 2011. Sparse polynomial division using a heap. J. Symb. Comput. 46, 7 (2011), 807--822.
[46]
Marc Moreno Maza. 1999. On Triangular Decompositions of Algebraic Varieties. Technical Report TR 4/99. NAG Ltd, Oxford, UK. Presented at the MEGA-2000 Conference, Bath, England. http://www.csd.uwo.ca/?moreno.
[47]
Marc Moreno Maza and Jean-Louis Roch (Eds.). 2010. Proceedings of the 4th International Workshop on Parallel Symbolic Computation, PASCO 2010, July 21-23, 2010, Grenoble, France. ACM.
[48]
Marc Moreno Maza and Stephen M. Watt (Eds.). 2007. Proceedings of the 3rd International Workshop on Parallel Symbolic Computation, PASCO 2007, 27-28 July 2007, London, Ontario, Canada. ACM.
[49]
Marc Moreno Maza and Yuzhen Xie. 2011. Balanced Dense Polynomial Multiplication on Multi-Cores. Int. J. Found. Comput. Sci. 22, 5 (2011), 1035--1055.
[50]
John Nickolls, Ian Buck, Michael Garland, and Kevin Skadron. 2008. Scalable Parallel Programming with CUDA. Queue 6, 2 (2008), 40--53.
[51]
Naila Rahman and Rajeev Raman. 2000. Analysing Cache Effects in Distribution Sorting. ACM J. Exp. Algorithmics 5 (2000), 14.
[52]
John E. Savage. 1998. Models of computation - exploring the power of computing. Addison-Wesley.
[53]
Jaewoong Sim, Aniruddha Dasgupta, Hyesoon Kim, and Richard W. Vuduc. 2012. A performance analysis framework for identifying potential benefits in GPGPU applications. In PPOPP 2012, New Orleans, LA, USA, February 25--29, 2012.
[54]
Charles Van Loan. 1992. Computational frameworks for the fast Fourier transform. SIAM.
[55]
Joachim von zur Gathen and Jürgen Gerhard. 2013. Modern Computer Algebra (3. ed.). Cambridge University Press.
[56]
Wen-tsun Wu. 1987. A zero structure theorem for polynomial-equations-solving and its applications. In EUROCAL '87, Proceedings (LNCS), Vol. 378. Springer, 44.
[57]
Richard Zippel (Ed.). 1992. Computer Algebra and Parallelism, Second International Workshop, Ithaca, USA, May 9--11, 1990. LNCS, Vol. 584. Springer
Index Terms
- Design and Implementation of Multi-Threaded Algorithms in Polynomial Algebra
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View all- van der Hoeven JMaza MZhi L(2022)On the Complexity of Symbolic ComputationProceedings of the 2022 International Symposium on Symbolic and Algebraic Computation10.1145/3476446.3535493(3-12)Online publication date: 4-Jul-2022
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