Optimal systolic array algorithms for tensor product
In this paper we examine the computational complexity of optimal systolic array algorithms for tensor product. We provide a time minimal schedule that meets the computed processor lower and upper bounds including one for tensor product. Our principle contribution is to find lower and upper bounds in...
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| Published in | Applied mathematics and computation Vol. 168; no. 1; pp. 496 - 518 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
Elsevier Inc
01.09.2005
Elsevier |
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| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2004.09.045 |
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| Abstract | In this paper we examine the computational complexity of optimal systolic array algorithms for tensor product. We provide a time minimal schedule that meets the computed processor lower and upper bounds including one for tensor product. Our principle contribution is to find lower and upper bounds in the algorithm and its implementation for generating function and find processor-time-minimal schedule. |
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| AbstractList | In this paper we examine the computational complexity of optimal systolic array algorithms for tensor product. We provide a time minimal schedule that meets the computed processor lower and upper bounds including one for tensor product. Our principle contribution is to find lower and upper bounds in the algorithm and its implementation for generating function and find processor-time-minimal schedule. |
| Author | Mishra, P.K. |
| Author_xml | – sequence: 1 givenname: P.K. surname: Mishra fullname: Mishra, P.K. email: pkmishra@ieee.org, mishra_pkumar@yahoo.com organization: Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835 215, India |
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| Cites_doi | 10.1137/0203021 10.1109/TASSP.1987.1165233 10.1090/ulect/008 10.1142/S0129054198000295 10.1109/12.48870 10.1016/0743-7315(89)90018-X 10.1007/BF00925828 10.1145/321406.321418 10.1145/367766.368168 10.1109/ASAP.1995.522902 10.1007/BF02253318 10.1145/360827.360844 10.1109/TC.1985.1676516 10.1016/0097-3165(95)90067-5 10.1215/S0012-7094-73-04054-4 10.1016/0167-8191(90)90044-A 10.1145/800015.808184 10.1137/0114108 10.1109/PROC.1983.12532 10.1007/3-540-17179-7_30 10.1109/78.175736 10.1109/71.113078 10.1109/TC.1987.1676945 10.1016/0167-8191(90)90133-T 10.1016/0743-7315(85)90029-2 10.1007/BF02309554 10.1016/S0167-8191(05)80150-4 10.1109/12.90251 10.1109/71.277790 10.1023/A:1008069920230 10.1109/71.139200 |
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| Keywords | Lower and upper bounds Tensor product Computational complexity Systolic algorithms Lower bound Upper bound Generating function Optimal algorithm Applied mathematics |
| Language | English |
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| References | Krishnamurthy, Kunde, Schimmler, Schroder (bib28) 1990; 13 Le Verge, Mauras, Quinton (bib55) 1991; 3 Karp, Miller, Winograd (bib27) 1967; 14 Ullman (bib54) 1984 P.R. Cappello, K. Steiglitz, Unifying VLSI array design with linear transformations, in: H.J. Siegel, L. Siegel, (Eds.), Proc. Int. Conf. on Parallel Processing, Bellaire, MI, August 1983, pp. 448–457. Li, Wah (bib25) 1985; C-34 Krishnamurthy, Schroder (bib29) 1991; 17 Kung, Leiserson (bib30) 1980 Darte, Khachiyan, Robert (bib14) 1992 Benaini, Robert (bib2) 1990; 15 Fortes, Fu, Wah (bib17) 1988 Ibarra, Palis (bib24) 1987; ASSP-35 Y. Robert, D. Trystram, An orthogonal systolic array for the algebraic path problem, in: Int. Workshop Systolic Arrays, 1986. Karrp, Miller, Winograd (bib26) 1966; 14 Louka, Tchuente (bib34) 1989 Engstrom, Cappello (bib15) 1989; 7 Stanley (bib50) 1973; 40 Kung, Sheng-chun Lo, Lewis (bib31) 1987; 36 . Shang, Fortes (bib49) 1991; 40 Fortes, Parisi-Presicce (bib19) 1984 Sahni (bib43) 1974; 3 Scheiman, Cappello (bib46) 1990 Hirschberg (bib23) 1983 Granata, Conner, Tolimieri (bib21) 1992; 40 Cappello (bib9) 1989 P. Quinton, Automatic synthesis of systolic arrays from uniform recurrent equations, in: Proc. 11th Symp. on Computer Architecture, 1984, pp. 208–214. D.K. Wilde, A library for doing polyhedral operations, Master’s thesis, Corvallis, Oregon, December 1993, Also published as IRISA technical report PI 785, Rennes, France, December 1993. Clauss, Mongenet, Perrin (bib12) 1990 MacMahon (bib36) 1979; vol. I C. Scheiman, P. Cappello, A processor-time minimal systolic array for the 3D rectilinear mesh, in: Proc. Int. Conf. On Application Specific Array Processors, Strasbourg, France, July 1995, pp. 26–33. B. Sturmfels, Gröbner Bases and Convex Polytopes, AMS University Lecture Series, Providence, RI, 1995. Lin, Prasanna Kumar (bib33) 1990; 39 Floyd (bib16) 1962; 5 Benaini, Robert (bib3) 1990 Rajopadhye, Purushothaman, Fujimoto (bib40) 1986; vol. 241 Rote (bib42) 1985; 34 December 1993. Scheiman, Cappello (bib47) 1992; 3 Warshall (bib56) 1962; 9 Aho, Hopcroft, Ullman (bib1) 1974 MacMahon (bib35) 1979; vol. I Benaini, Robert, Tourancheau (bib4) 1989 Wong, Delosme (bib59) 1992 Garey, Johnson (bib20) 1979 Y. Wong, J.-M. Delosme, Optimization of processor count for systolic arrays, Department of Computer Science, RR-697, Yale University, May 1989. Moldovan (bib38) 1983; 71 Guibas, Kung, Thompson (bib22) 1979 Scheiman, Cappello (bib48) 1994; 5 P. Cappello, Ömer Eğecioğlu, C. Scheiman, Processor-time-optimal systolic arrays, J. Parallel Algorithms Appl. Cappello, Steiglitz (bib11) 1984; vol. 2 MacMahon (bib37) 1979; vol. I Cappello, Ömer Egˇeciogˇlu (bib6) 1998; 9 Kai Hwang, Faye A. Briggss, Computer Architecture and Parallel Processing, McGraw-Hill series in computer organization and architecture, 1985. A.P. Petitet, J.J. Dongarra, Algorithmic redistribution methods for block cyclic decompositions. February 1998 Fortes, Moldovan (bib18) 1985; 2 Clauss, Loechner (bib13) 1998; 19 P.R. Cappello, VLSI architectures for digital signal processing. Ph.D. thesis, Princeton University, Princeton, NJ, October 1982. Strumfels (bib53) 1995; 72 Lamport (bib32) 1974; 17 Down (bib62) 1993 C. Scheiman, Mapping fundamental algorithms onto multiprocessor architectures. Ph.D. thesis, UC Santa Barbara, Department of Computer Science Stanley (bib51) 1986 Cappello (bib5) 1992; 3 Cappello (10.1016/j.amc.2004.09.045_bib5) 1992; 3 10.1016/j.amc.2004.09.045_bib52 10.1016/j.amc.2004.09.045_bib10 10.1016/j.amc.2004.09.045_bib57 Fortes (10.1016/j.amc.2004.09.045_bib17) 1988 Ibarra (10.1016/j.amc.2004.09.045_bib24) 1987; ASSP-35 MacMahon (10.1016/j.amc.2004.09.045_bib37) 1979; vol. I Rote (10.1016/j.amc.2004.09.045_bib42) 1985; 34 Guibas (10.1016/j.amc.2004.09.045_bib22) 1979 Moldovan (10.1016/j.amc.2004.09.045_bib38) 1983; 71 Floyd (10.1016/j.amc.2004.09.045_bib16) 1962; 5 Hirschberg (10.1016/j.amc.2004.09.045_bib23) 1983 Strumfels (10.1016/j.amc.2004.09.045_bib53) 1995; 72 Clauss (10.1016/j.amc.2004.09.045_bib12) 1990 Lin (10.1016/j.amc.2004.09.045_bib33) 1990; 39 10.1016/j.amc.2004.09.045_bib41 Rajopadhye (10.1016/j.amc.2004.09.045_bib40) 1986; vol. 241 10.1016/j.amc.2004.09.045_bib44 10.1016/j.amc.2004.09.045_bib45 Benaini (10.1016/j.amc.2004.09.045_bib2) 1990; 15 10.1016/j.amc.2004.09.045_bib7 10.1016/j.amc.2004.09.045_bib8 Fortes (10.1016/j.amc.2004.09.045_bib19) 1984 MacMahon (10.1016/j.amc.2004.09.045_bib36) 1979; vol. I Darte (10.1016/j.amc.2004.09.045_bib14) 1992 Cappello (10.1016/j.amc.2004.09.045_bib6) 1998; 9 Le Verge (10.1016/j.amc.2004.09.045_bib55) 1991; 3 10.1016/j.amc.2004.09.045_bib39 Aho (10.1016/j.amc.2004.09.045_bib1) 1974 Shang (10.1016/j.amc.2004.09.045_bib49) 1991; 40 Down (10.1016/j.amc.2004.09.045_bib62) 1993 Krishnamurthy (10.1016/j.amc.2004.09.045_bib29) 1991; 17 MacMahon (10.1016/j.amc.2004.09.045_bib35) 1979; vol. I Karp (10.1016/j.amc.2004.09.045_bib27) 1967; 14 Garey (10.1016/j.amc.2004.09.045_bib20) 1979 Lamport (10.1016/j.amc.2004.09.045_bib32) 1974; 17 Karrp (10.1016/j.amc.2004.09.045_bib26) 1966; 14 Scheiman (10.1016/j.amc.2004.09.045_bib47) 1992; 3 Stanley (10.1016/j.amc.2004.09.045_bib51) 1986 Warshall (10.1016/j.amc.2004.09.045_bib56) 1962; 9 10.1016/j.amc.2004.09.045_bib61 Granata (10.1016/j.amc.2004.09.045_bib21) 1992; 40 Li (10.1016/j.amc.2004.09.045_bib25) 1985; C-34 Fortes (10.1016/j.amc.2004.09.045_bib18) 1985; 2 Kung (10.1016/j.amc.2004.09.045_bib30) 1980 Benaini (10.1016/j.amc.2004.09.045_bib3) 1990 Stanley (10.1016/j.amc.2004.09.045_bib50) 1973; 40 Scheiman (10.1016/j.amc.2004.09.045_bib48) 1994; 5 Clauss (10.1016/j.amc.2004.09.045_bib13) 1998; 19 Sahni (10.1016/j.amc.2004.09.045_bib43) 1974; 3 10.1016/j.amc.2004.09.045_bib60 Cappello (10.1016/j.amc.2004.09.045_bib9) 1989 Kung (10.1016/j.amc.2004.09.045_bib31) 1987; 36 Ullman (10.1016/j.amc.2004.09.045_bib54) 1984 Cappello (10.1016/j.amc.2004.09.045_bib11) 1984; vol. 2 Krishnamurthy (10.1016/j.amc.2004.09.045_bib28) 1990; 13 Louka (10.1016/j.amc.2004.09.045_bib34) 1989 Engstrom (10.1016/j.amc.2004.09.045_bib15) 1989; 7 10.1016/j.amc.2004.09.045_bib58 Wong (10.1016/j.amc.2004.09.045_bib59) 1992 Benaini (10.1016/j.amc.2004.09.045_bib4) 1989 Scheiman (10.1016/j.amc.2004.09.045_bib46) 1990 |
| References_xml | – reference: C. Scheiman, Mapping fundamental algorithms onto multiprocessor architectures. Ph.D. thesis, UC Santa Barbara, Department of Computer Science, – start-page: 4 year: 1990 end-page: 18 ident: bib12 article-title: Calculus of space-optimal mappings of systolic algorithms on processor arrays publication-title: Proc. Int. Conf. on Application Specific Array Processors – volume: 36 start-page: 603 year: 1987 end-page: 614 ident: bib31 article-title: Optimal systolic design for the transitive closure and the shortest path problem publication-title: IEEE Trans. Comput. – reference: P.R. Cappello, K. Steiglitz, Unifying VLSI array design with linear transformations, in: H.J. Siegel, L. Siegel, (Eds.), Proc. Int. Conf. on Parallel Processing, Bellaire, MI, August 1983, pp. 448–457. – volume: vol. I start-page: 1212 year: 1979 end-page: 1232 ident: bib35 article-title: The diophantine inequality publication-title: Collected Papers – volume: 5 year: 1962 ident: bib16 article-title: Algorithm 97: shortest path publication-title: Commun. ACM – start-page: 37 year: 1992 end-page: 46 ident: bib14 article-title: Linear scheduling is close to optimal publication-title: Application Specific Array Processors – volume: vol. 2 start-page: 23 year: 1984 end-page: 65 ident: bib11 article-title: Unifying VLSI array design with linear transformations of space-time publication-title: Advances in Computing Research, VLSI Theory – start-page: 322 year: 1984 end-page: 328 ident: bib19 article-title: Optimal linear schedules for the parallel execution of algorithms publication-title: Int. Conf. Parallel Processing – reference: , December 1993. – volume: 19 start-page: 179 year: 1998 end-page: 194 ident: bib13 article-title: Parametric analysis of polyhedral iteration spaces publication-title: J. VLSI Signal Process. – start-page: 73 year: 1989 end-page: 82 ident: bib4 article-title: A new systolic architecture for the algebraic path problem publication-title: Systolic Array Processors – volume: 15 start-page: 211 year: 1990 end-page: 225 ident: bib2 article-title: Space-time-minimal systolic arrays for Gaussian elimination and the algebraic path problem publication-title: Parallel Comput. – start-page: 509 year: 1979 end-page: 525 ident: bib22 article-title: Direct VLSI implementation of combinatorial algorithms publication-title: Proc. Caltech Conf. on VLSI – volume: 40 start-page: 723 year: 1991 end-page: 742 ident: bib49 article-title: Time optimal linear schedule for algorithms with uniform dependencies publication-title: IEEE Trans. Comput. – reference: A.P. Petitet, J.J. Dongarra, Algorithmic redistribution methods for block cyclic decompositions. February 1998, – volume: 14 start-page: 563 year: 1967 end-page: 590 ident: bib27 article-title: The organization of computations for uniform recurrence equations publication-title: J. ACM – reference: C. Scheiman, P. Cappello, A processor-time minimal systolic array for the 3D rectilinear mesh, in: Proc. Int. Conf. On Application Specific Array Processors, Strasbourg, France, July 1995, pp. 26–33. – volume: 3 start-page: 257 year: 1992 end-page: 269 ident: bib47 article-title: A processor-time minimal systolic array for transitive closure publication-title: IEEE Trans. Parallel Distributed Syst. – year: 1986 ident: bib51 article-title: Enumerative Combinatorics, vol. I – volume: 9 year: 1962 ident: bib56 article-title: A theorem on Boolean matrices publication-title: J. ACM – start-page: 271 year: 1980 end-page: 292 ident: bib30 article-title: Algorithms for VLSI processor arrays publication-title: Introduction to VLSI Systems – year: 1979 ident: bib20 article-title: Computers and Intractability: A Guide to the Theory of NP-Completeness – year: 1974 ident: bib1 article-title: The Design and Analysis of Computer Algorithms – start-page: 347 year: 1989 end-page: 356 ident: bib9 article-title: A spacetime-minimal systolic array for matrix product publication-title: Systolic Array Processors – reference: B. Sturmfels, Gröbner Bases and Convex Polytopes, AMS University Lecture Series, Providence, RI, 1995. – volume: vol. I start-page: 1233 year: 1979 end-page: 1246 ident: bib37 article-title: Note on the diophantine inequality publication-title: Collected Papers – volume: 7 start-page: 201 year: 1989 end-page: 231 ident: bib15 article-title: The SDEF programming system publication-title: J. Parallel Distributed Comput. – reference: Y. Robert, D. Trystram, An orthogonal systolic array for the algebraic path problem, in: Int. Workshop Systolic Arrays, 1986. – volume: vol. 241 start-page: 488 year: 1986 end-page: 503 ident: bib40 article-title: On synthesizing systolic arrays from recurrence equations with linear dependencies publication-title: Lecture Notes in Computer Science – start-page: 454 year: 1988 end-page: 494 ident: bib17 article-title: Systematic design approaches for algorithmically specified systolic arrays publication-title: Computer Architecture: Concepts and Systems – volume: 40 start-page: 607 year: 1973 end-page: 632 ident: bib50 article-title: Linear homogeneous diophantine equations and magic labelings of graphs publication-title: Duke Math. J. – volume: 39 start-page: 393 year: 1990 end-page: 399 ident: bib33 article-title: A note on the linear transformation method for systolic array design publication-title: IEEE Trans. Comput. – reference: Kai Hwang, Faye A. Briggss, Computer Architecture and Parallel Processing, McGraw-Hill series in computer organization and architecture, 1985. – volume: ASSP-35 start-page: 1046 year: 1987 end-page: 1064 ident: bib24 article-title: VLSI algorithms for solving recurrence equations and applications publication-title: IEEE Trans. Acoust, Speech, Signal Process. – start-page: 19 year: 1990 end-page: 30 ident: bib46 article-title: A processor-time minimal systolic array for transitive closure publication-title: Proc. Int Conf. on Application Specific Array Processors – volume: 17 start-page: 83 year: 1974 end-page: 93 ident: bib32 article-title: The parallel execution of Do-Loops publication-title: Commun. ACM – reference: Y. Wong, J.-M. Delosme, Optimization of processor count for systolic arrays, Department of Computer Science, RR-697, Yale University, May 1989. – volume: 3 start-page: 4 year: 1992 end-page: 13 ident: bib5 article-title: A processor-time-minimal systolic array for cubical meshalgorithms publication-title: IEEE Trans. Parallel Distributed Syst. – volume: 40 start-page: 2921 year: 1992 end-page: 2930 ident: bib21 article-title: Recursive fast algorithm and the role of the tensor product publication-title: IEEE Trans. Signal Process. – volume: vol. I start-page: 1138 year: 1979 end-page: 1188 ident: bib36 article-title: Memoir on the theory of the partitions of numbers-Part II publication-title: Collected Papers – volume: 71 start-page: 113 year: 1983 end-page: 120 ident: bib38 article-title: On the design of algorithms for VLSI systolic arrays publication-title: Proc. IEEE – volume: 9 start-page: 351 year: 1998 end-page: 375 ident: bib6 article-title: Processor lower bound formulas for array computations and parametric Diophantine systems publication-title: Int. J. Found. Comput. Sci. – start-page: 264 year: 1989 end-page: 274 ident: bib34 article-title: An optimal solution for Gauss–Jordon elimination on 2D systolic arrays publication-title: Systolic Array Processors – volume: 17 start-page: 483 year: 1991 end-page: 492 ident: bib29 article-title: Systolic algorithm for multivariable approximation using tensor products of basis functions publication-title: Parallel Comput. – year: 1984 ident: bib54 article-title: Computational Aspects of VLSI – volume: C-34 start-page: 66 year: 1985 end-page: 77 ident: bib25 article-title: The design of optimal systolic algorithms publication-title: IEEE Trans. Comput. – volume: 3 start-page: 262 year: 1974 end-page: 279 ident: bib43 article-title: Computational related problems publication-title: SIAM J. Comput. – reference: . – reference: P.R. Cappello, VLSI architectures for digital signal processing. Ph.D. thesis, Princeton University, Princeton, NJ, October 1982. – reference: P. Quinton, Automatic synthesis of systolic arrays from uniform recurrent equations, in: Proc. 11th Symp. on Computer Architecture, 1984, pp. 208–214. – start-page: 746 year: 1990 end-page: 757 ident: bib3 article-title: Spacetime-minimal systolic arrays for gaussian elimination and the algebraic path problem publication-title: Proc. Int. Conf. On Application Specific Array Processors – volume: 72 start-page: 302 year: 1995 end-page: 309 ident: bib53 article-title: On vector partition functions publication-title: J. Combinatorial Theory, Ser. A – reference: P. Cappello, Ömer Eğecioğlu, C. Scheiman, Processor-time-optimal systolic arrays, J. Parallel Algorithms Appl. – volume: 13 start-page: 301 year: 1990 end-page: 308 ident: bib28 article-title: Systolic algorithm for tensor products of matrices: implementation and applications publication-title: Parallel Comput. – start-page: 275 year: 1992 end-page: 282 ident: bib59 article-title: Space-optimal linear processor allocation for systolic array synthesis publication-title: Proc. 6th Int. Parallel Processing Symp. – volume: 2 start-page: 277 year: 1985 end-page: 301 ident: bib18 article-title: Parallelism detection and algorithm transformation techniques useful for VLSI architecture design publication-title: J. Parallel Distributed Comput. – volume: 34 start-page: 191 year: 1985 end-page: 219 ident: bib42 article-title: A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion) publication-title: Computing – reference: D.K. Wilde, A library for doing polyhedral operations, Master’s thesis, Corvallis, Oregon, December 1993, Also published as IRISA technical report PI 785, Rennes, France, December 1993. – volume: 5 start-page: 274 year: 1994 end-page: 280 ident: bib48 article-title: A period-processor-time-minimal schedule for cubical mesh algorithms publication-title: IEEE Trans. Parallel Distributed Syst. – year: 1983 ident: bib23 article-title: Recent results on the complexity of common-subsequence problems publication-title: Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison – volume: 3 start-page: 173 year: 1991 end-page: 182 ident: bib55 article-title: The ALPHA language and its use for the design of systolic arrays publication-title: J. VLSI Signal Process. – volume: 14 start-page: 1390 year: 1966 end-page: 1411 ident: bib26 article-title: Properties of a model for parallel computations: determinacy, termination, queueing publication-title: SIAM J. Appl. Math. – year: 1993 ident: bib62 article-title: High Performance Computing – volume: 9 issue: Jan year: 1962 ident: 10.1016/j.amc.2004.09.045_bib56 article-title: A theorem on Boolean matrices publication-title: J. ACM – volume: 3 start-page: 262 year: 1974 ident: 10.1016/j.amc.2004.09.045_bib43 article-title: Computational related problems publication-title: SIAM J. Comput. doi: 10.1137/0203021 – volume: ASSP-35 start-page: 1046 issue: 7 year: 1987 ident: 10.1016/j.amc.2004.09.045_bib24 article-title: VLSI algorithms for solving recurrence equations and applications publication-title: IEEE Trans. Acoust, Speech, Signal Process. doi: 10.1109/TASSP.1987.1165233 – volume: vol. I start-page: 1138 year: 1979 ident: 10.1016/j.amc.2004.09.045_bib36 article-title: Memoir on the theory of the partitions of numbers-Part II – start-page: 347 year: 1989 ident: 10.1016/j.amc.2004.09.045_bib9 article-title: A spacetime-minimal systolic array for matrix product – ident: 10.1016/j.amc.2004.09.045_bib52 doi: 10.1090/ulect/008 – ident: 10.1016/j.amc.2004.09.045_bib61 – volume: 9 start-page: 351 issue: 4 year: 1998 ident: 10.1016/j.amc.2004.09.045_bib6 article-title: Processor lower bound formulas for array computations and parametric Diophantine systems publication-title: Int. J. Found. Comput. Sci. doi: 10.1142/S0129054198000295 – volume: 39 start-page: 393 issue: 3 year: 1990 ident: 10.1016/j.amc.2004.09.045_bib33 article-title: A note on the linear transformation method for systolic array design publication-title: IEEE Trans. Comput. doi: 10.1109/12.48870 – volume: vol. I start-page: 1212 year: 1979 ident: 10.1016/j.amc.2004.09.045_bib35 article-title: The diophantine inequality λx⩾μy. – year: 1974 ident: 10.1016/j.amc.2004.09.045_bib1 – year: 1986 ident: 10.1016/j.amc.2004.09.045_bib51 – year: 1984 ident: 10.1016/j.amc.2004.09.045_bib54 – volume: 7 start-page: 201 year: 1989 ident: 10.1016/j.amc.2004.09.045_bib15 article-title: The SDEF programming system publication-title: J. Parallel Distributed Comput. doi: 10.1016/0743-7315(89)90018-X – volume: 3 start-page: 173 year: 1991 ident: 10.1016/j.amc.2004.09.045_bib55 article-title: The ALPHA language and its use for the design of systolic arrays publication-title: J. VLSI Signal Process. doi: 10.1007/BF00925828 – volume: 14 start-page: 563 year: 1967 ident: 10.1016/j.amc.2004.09.045_bib27 article-title: The organization of computations for uniform recurrence equations publication-title: J. ACM doi: 10.1145/321406.321418 – volume: 5 year: 1962 ident: 10.1016/j.amc.2004.09.045_bib16 article-title: Algorithm 97: shortest path publication-title: Commun. ACM doi: 10.1145/367766.368168 – ident: 10.1016/j.amc.2004.09.045_bib45 doi: 10.1109/ASAP.1995.522902 – year: 1983 ident: 10.1016/j.amc.2004.09.045_bib23 article-title: Recent results on the complexity of common-subsequence problems – ident: 10.1016/j.amc.2004.09.045_bib58 – ident: 10.1016/j.amc.2004.09.045_bib60 – volume: 34 start-page: 191 issue: 3 year: 1985 ident: 10.1016/j.amc.2004.09.045_bib42 article-title: A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion) publication-title: Computing doi: 10.1007/BF02253318 – year: 1979 ident: 10.1016/j.amc.2004.09.045_bib20 – volume: 17 start-page: 83 issue: 2 year: 1974 ident: 10.1016/j.amc.2004.09.045_bib32 article-title: The parallel execution of Do-Loops publication-title: Commun. ACM doi: 10.1145/360827.360844 – volume: C-34 start-page: 66 issue: 1 year: 1985 ident: 10.1016/j.amc.2004.09.045_bib25 article-title: The design of optimal systolic algorithms publication-title: IEEE Trans. Comput. doi: 10.1109/TC.1985.1676516 – start-page: 73 year: 1989 ident: 10.1016/j.amc.2004.09.045_bib4 article-title: A new systolic architecture for the algebraic path problem – volume: 72 start-page: 302 year: 1995 ident: 10.1016/j.amc.2004.09.045_bib53 article-title: On vector partition functions publication-title: J. Combinatorial Theory, Ser. A doi: 10.1016/0097-3165(95)90067-5 – year: 1993 ident: 10.1016/j.amc.2004.09.045_bib62 – volume: 40 start-page: 607 year: 1973 ident: 10.1016/j.amc.2004.09.045_bib50 article-title: Linear homogeneous diophantine equations and magic labelings of graphs publication-title: Duke Math. J. doi: 10.1215/S0012-7094-73-04054-4 – volume: 15 start-page: 211 year: 1990 ident: 10.1016/j.amc.2004.09.045_bib2 article-title: Space-time-minimal systolic arrays for Gaussian elimination and the algebraic path problem publication-title: Parallel Comput. doi: 10.1016/0167-8191(90)90044-A – ident: 10.1016/j.amc.2004.09.045_bib39 doi: 10.1145/800015.808184 – volume: 14 start-page: 1390 year: 1966 ident: 10.1016/j.amc.2004.09.045_bib26 article-title: Properties of a model for parallel computations: determinacy, termination, queueing publication-title: SIAM J. Appl. Math. doi: 10.1137/0114108 – volume: 71 start-page: 113 issue: 1 year: 1983 ident: 10.1016/j.amc.2004.09.045_bib38 article-title: On the design of algorithms for VLSI systolic arrays publication-title: Proc. IEEE doi: 10.1109/PROC.1983.12532 – volume: vol. 241 start-page: 488 year: 1986 ident: 10.1016/j.amc.2004.09.045_bib40 article-title: On synthesizing systolic arrays from recurrence equations with linear dependencies doi: 10.1007/3-540-17179-7_30 – volume: 40 start-page: 2921 issue: 12 year: 1992 ident: 10.1016/j.amc.2004.09.045_bib21 article-title: Recursive fast algorithm and the role of the tensor product publication-title: IEEE Trans. Signal Process. doi: 10.1109/78.175736 – ident: 10.1016/j.amc.2004.09.045_bib44 – ident: 10.1016/j.amc.2004.09.045_bib7 – start-page: 4 year: 1990 ident: 10.1016/j.amc.2004.09.045_bib12 article-title: Calculus of space-optimal mappings of systolic algorithms on processor arrays – start-page: 37 year: 1992 ident: 10.1016/j.amc.2004.09.045_bib14 article-title: Linear scheduling is close to optimal – volume: vol. I start-page: 1233 year: 1979 ident: 10.1016/j.amc.2004.09.045_bib37 article-title: Note on the diophantine inequality λx⩾μy – volume: 3 start-page: 4 issue: 1 year: 1992 ident: 10.1016/j.amc.2004.09.045_bib5 article-title: A processor-time-minimal systolic array for cubical meshalgorithms publication-title: IEEE Trans. Parallel Distributed Syst. doi: 10.1109/71.113078 – volume: 36 start-page: 603 issue: 5 year: 1987 ident: 10.1016/j.amc.2004.09.045_bib31 article-title: Optimal systolic design for the transitive closure and the shortest path problem publication-title: IEEE Trans. Comput. doi: 10.1109/TC.1987.1676945 – ident: 10.1016/j.amc.2004.09.045_bib57 – volume: 13 start-page: 301 issue: 3 year: 1990 ident: 10.1016/j.amc.2004.09.045_bib28 article-title: Systolic algorithm for tensor products of matrices: implementation and applications publication-title: Parallel Comput. doi: 10.1016/0167-8191(90)90133-T – start-page: 746 year: 1990 ident: 10.1016/j.amc.2004.09.045_bib3 article-title: Spacetime-minimal systolic arrays for gaussian elimination and the algebraic path problem – volume: 2 start-page: 277 year: 1985 ident: 10.1016/j.amc.2004.09.045_bib18 article-title: Parallelism detection and algorithm transformation techniques useful for VLSI architecture design publication-title: J. Parallel Distributed Comput. doi: 10.1016/0743-7315(85)90029-2 – ident: 10.1016/j.amc.2004.09.045_bib41 doi: 10.1007/BF02309554 – start-page: 264 year: 1989 ident: 10.1016/j.amc.2004.09.045_bib34 article-title: An optimal solution for Gauss–Jordon elimination on 2D systolic arrays – volume: 17 start-page: 483 issue: 4–5 year: 1991 ident: 10.1016/j.amc.2004.09.045_bib29 article-title: Systolic algorithm for multivariable approximation using tensor products of basis functions publication-title: Parallel Comput. doi: 10.1016/S0167-8191(05)80150-4 – start-page: 271 year: 1980 ident: 10.1016/j.amc.2004.09.045_bib30 article-title: Algorithms for VLSI processor arrays – start-page: 509 year: 1979 ident: 10.1016/j.amc.2004.09.045_bib22 article-title: Direct VLSI implementation of combinatorial algorithms publication-title: Proc. Caltech Conf. on VLSI – volume: vol. 2 start-page: 23 year: 1984 ident: 10.1016/j.amc.2004.09.045_bib11 article-title: Unifying VLSI array design with linear transformations of space-time – start-page: 275 year: 1992 ident: 10.1016/j.amc.2004.09.045_bib59 article-title: Space-optimal linear processor allocation for systolic array synthesis – ident: 10.1016/j.amc.2004.09.045_bib8 – volume: 40 start-page: 723 issue: 6 year: 1991 ident: 10.1016/j.amc.2004.09.045_bib49 article-title: Time optimal linear schedule for algorithms with uniform dependencies publication-title: IEEE Trans. Comput. doi: 10.1109/12.90251 – ident: 10.1016/j.amc.2004.09.045_bib10 – start-page: 19 year: 1990 ident: 10.1016/j.amc.2004.09.045_bib46 article-title: A processor-time minimal systolic array for transitive closure – start-page: 454 year: 1988 ident: 10.1016/j.amc.2004.09.045_bib17 article-title: Systematic design approaches for algorithmically specified systolic arrays – volume: 5 start-page: 274 issue: 3 year: 1994 ident: 10.1016/j.amc.2004.09.045_bib48 article-title: A period-processor-time-minimal schedule for cubical mesh algorithms publication-title: IEEE Trans. Parallel Distributed Syst. doi: 10.1109/71.277790 – volume: 19 start-page: 179 year: 1998 ident: 10.1016/j.amc.2004.09.045_bib13 article-title: Parametric analysis of polyhedral iteration spaces publication-title: J. VLSI Signal Process. doi: 10.1023/A:1008069920230 – start-page: 322 year: 1984 ident: 10.1016/j.amc.2004.09.045_bib19 article-title: Optimal linear schedules for the parallel execution of algorithms publication-title: Int. Conf. Parallel Processing – volume: 3 start-page: 257 issue: 3 year: 1992 ident: 10.1016/j.amc.2004.09.045_bib47 article-title: A processor-time minimal systolic array for transitive closure publication-title: IEEE Trans. Parallel Distributed Syst. doi: 10.1109/71.139200 |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Computational complexity Computer science; control theory; systems Exact sciences and technology Lower and upper bounds Systolic algorithms Tensor product Theoretical computing |
| Title | Optimal systolic array algorithms for tensor product |
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