Matrix multiplication via arithmetic progressions

On Sets of Integers Which Contain No Three Terms in Arithmetical Progression

Behrend, F. A. (1946) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.32.12.331 · Cited by 414

Partial and Total Matrix Multiplication

Schönhage, A. (1981) · SIAM Journal on Computing · doi:10.1137/0210032 · Cited by 279

On the Asymptotic Complexity of Matrix Multiplication

Coppersmith, D., & Winograd, S. (1982) · SIAM Journal on Computing · doi:10.1137/0211038 · Cited by 221

How to Multiply Matrices Faster

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On Sets of Integers Which Contain No Three Terms in Arithmetical Progression

Salem, R., & Spencer, D. C. (1942) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.28.12.561 · Cited by 134

Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations

Pan, V. Y. (1978) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1978.34 · Cited by 121

The asymptotic spectrum of tensors and the exponent of matrix multiplication

Strassen, V. (1986) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1986.52 · Cited by 120

Parallel Hill Cipher Encryption Algorithm

Haj, M., & Qatawneh, M. (2018) · International Journal of Computer Applications · doi:10.5120/ijca2018916326 · Cited by 14

Nondecreasing paths in a weighted graph or

Williams, V. V. (2010) · ACM Transactions on Algorithms · doi:10.1145/1824777.1824790 · Cited by 14

Solving Linear Systems through Nested Dissection

Alon, N., & Yuster, R. (2010) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2010.28 · Cited by 14

Privacy Preserving Support Vector Machine Using Non-linear Kernels on Hadoop Mahout

Teo, S. G., Han, S., & Lee, V. C. S. (2013) · IEEE International Conference on Computational Science and Engineering (CSE) · doi:10.1109/cse.2013.200 · Cited by 14

Almost Optimal (on the average) Combinatorial Algorithms for Boolean Matrix Product Witnesses, Computing the Diameter (Extended Abstract)

Schnorr, C. P., & Subramanian, C. R. (1998) · Lecture notes in computer science · doi:10.1007/3-540-49543-6_18 · Cited by 14

Integer matrix rank certification

Storjohann, A. (2009) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1576702.1576748 · Cited by 14

Fast rectangular matrix multiplication and some applications

Ke, S., Zeng, B., Han, W., & Pan, V. Y. (2008) · Science in China Series A Mathematics · doi:10.1007/s11425-007-0169-2 · Cited by 14

Algorithms for generating convex sets in acyclic digraphs

Balister, P., Gerke, S., Gutin, G., Johnstone, A., Reddington, J., Scott, E. A., Soleimanfallah, A., & Yeo, A. (2008) · Journal of Discrete Algorithms · doi:10.1016/j.jda.2008.07.008 · Cited by 14

Estimation of reactivity and delayed neutron precursors’ concentrations using a multiscale extended Kalman filter

Patel, S. B., Mukhopadhyay, S., & Tiwari, A. P. (2017) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2017.09.033 · Cited by 14

An O(nm) time algorithm for finding the min length directed cycle in a graph

Orlin, J. B., & Sedeño‐Noda, A. (2017) · ACM-SIAM Symposium on Discrete Algorithms (SODA) · doi:10.1137/1.9781611974782.122 · Cited by 14

Least-Squares Fuzzy Transforms and Autoencoders: Some Remarks and Application

Tomasiello, S. (2020) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2020.3007442 · Cited by 14

Efficient Algorithms for Maximum Weight Matchings in General Graphs with Small Edge Weights

Huang, C.-C., & Kavitha, T. (2012) · ACM-SIAM Symposium on Discrete Algorithms (SODA) · doi:10.1137/1.9781611973099.110 · Cited by 14

ASYMPTOTICALLY EFFICIENT ALGORITHMS FOR THE FROBENIUS FORM

Eberly, W. (2000) · doi:10.11575/prism/30585 · Cited by 14

Algorithms for Computing the Triplet and Quartet Distances for Binary and General Trees

Sand, A., Holt, M. K., Johansen, J., Fagerberg, R., Brodal, G. S., Pedersen, C. R., & Mailund, T. (2013) · Biology · doi:10.3390/biology2041189 · Cited by 14

On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix

Pan, V. Y. (2006) · Journal of Mathematical Sciences · doi:10.1007/s10958-006-0118-6 · Cited by 14

Two characterisations of minimal triangulations of 2K2 -free graphs

Meister, D. (2006) · Discrete Mathematics · doi:10.1016/j.disc.2006.07.001 · Cited by 14

On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes

Beelen, P., Hoholdt, T., Nielsen, J. S. R., & Wu, Y. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2243800 · Cited by 14

Why does information-based complexity use the real number model?

Woźniakowski, H. (1999) · Theoretical Computer Science · doi:10.1016/s0304-3975(98)00300-4 · Cited by 14

Weighted Bipartite Matching in Matrix Multiplication Time

Sankowski, P. (2006) · Lecture notes in computer science · doi:10.1007/11786986_25 · Cited by 14

Pricing Discretely Monitored Barrier Options Under Markov Processes Using a Markov Chain Approximation

Cui, Z., & Taylor, S. M. (2019) · The Journal of Derivatives · doi:10.2139/ssrn.3382236 · Cited by 14

Two Algebraic Attacks Against the F-FCSRs Using the IV Mode

Berger, T. P., & Minier, M. (2005) · Lecture notes in computer science · doi:10.1007/11596219_12 · Cited by 14

The schur aggregation for solving linear systems of equations

Pan, V. Y., Murphy, B. S., Rosholt, R. E., & Tabanjeh, M. M. (2007) · Symbolic Numeric Computation · doi:10.1145/1277500.1277522 · Cited by 14

A simple greedy algorithm for finding functional relations: efficient implementation and average case analysis

Akutsu, T., Miyano, S., & Kuhara, S. (2003) · Theoretical Computer Science · doi:10.1016/s0304-3975(02)00183-4 · Cited by 14

Scalable Parallel Matrix Multiplication on Distributed Memory Parallel Computers

Li, K. (2001) · Journal of Parallel and Distributed Computing · doi:10.1006/jpdc.2001.1768 · Cited by 15

Efficient parallel independent subsets and matrix factorizations

Eberly, W. (2002) · IEEE Symposium on Parallel and Distributed Processing (SPDP) · doi:10.1109/spdp.1991.218278 · Cited by 14

Computing Elementary Symmetric Polynomials with a Subpolynomial Numberof Multiplications

Grolmusz, V. I. (2003) · SIAM Journal on Computing · doi:10.1137/s009753970342465x · Cited by 14

Parameterized complexity and polynomial-time approximation schemes

Huang, X., & Chen, J. (2004) · Cited by 14

Graph-Driven Free Parity BDDs: Algorithms and Lower Bounds

Brosenne, H., Homeister, M., & Waack, S. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44683-4_19 · Cited by 14

Sketches of a platypus: a survey of persistent homology and its algebraic foundations

Vejdemo‐Johansson, M. (2014) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/620/12371 · Cited by 14

Pebbling Game and Alternative Basis for High Performance Matrix Multiplication

Schwartz, O., & Vaknin, N. (2023) · SIAM Journal on Scientific Computing · doi:10.1137/22m1502719 · Cited by 19

Orthonormal Explicit Topic Analysis for Cross-Lingual Document Matching

McCrae, J. P., Cimiano, P., & Klinger, R. (2013) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/d13-1179 · Cited by 13

Approximating Shortest Paths in Graphs

Sen, S. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-00202-1_3 · Cited by 13

Control of ellipsoidal trajectories: Theory and numerical results

Kurzhanski, A. B., & Mesyats, A. I. (2014) · Computational Mathematics and Mathematical Physics · doi:10.1134/s0965542514030117 · Cited by 13

Ground state search by local and sequential updates of neural network quantum states

Zhang, W.-X., Xu, X., Wu, Z., Balachandran, V., & Poletti, D. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.165149 · Cited by 15

Using Recursion to Boost ATLAS’s Performance

D’Alberto, P., & Nicolau, A. E. (2008) · Springer eBooks · doi:10.1007/978-3-540-77704-5_12 · Cited by 13

Ant Colony Optimization With Combining Gaussian Eliminations for Matrix Multiplication

Zhou, Y., Lai, X., Li, Y., & Dong, W. (2012) · IEEE Transactions on Cybernetics · doi:10.1109/tsmcb.2012.2207717 · Cited by 13

Implementing the projected spatial rich features on a GPU

Ker, A. D. (2014) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2042473 · Cited by 13

Subquadratic zero-knowledge

Boyar, J., Gilles Brassard, A., & Peralta, R. (1995) · Journal of the ACM · doi:10.1145/227683.227686 · Cited by 13

Adaptive Information Coding for Secure and Reliable Wireless Telesurgery Communications

Tozal, M. E., Wang, Y., Al-Shaer, E. S., Saraç, K., Thuraisingham, B. M., & Chu, B.-T. B. (2011) · Mobile Networks and Applications · doi:10.1007/s11036-011-0333-3 · Cited by 13

Combinatorial and algebraic tools for optimal multilevel algorithms

Miller, G. L., & Koutis, I. (2007) · Cited by 13

Scheduling multiprocessor tasks on two parallel processors

Błażewicz, J., Dell’Olmo, P., & Drozdowski, M. (2002) · RAIRO - Operations Research · doi:10.1051/ro:2002004 · Cited by 13

Almost Exact Matchings

Yuster, R. (2011) · Algorithmica · doi:10.1007/s00453-011-9519-0 · Cited by 13

Classifying and querying very large taxonomies with bit-vector encoding

Aı̈t-Kaci, H., & Amir, S. (2015) · Journal of Intelligent Information Systems · doi:10.1007/s10844-015-0383-2 · Cited by 13

Nearly sparse linear algebra and application to discrete logarithms computations

Joux, A., & Pierrot, C. (2016) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814719261_0008 · Cited by 13

Algorithms for Inferring Context-Sensitive L-Systems

McQuillan, I., Bernard, J., & Prusinkiewicz, P. (2018) · Lecture notes in computer science · doi:10.1007/978-3-319-92435-9_9 · Cited by 13

Modified Graph Laplacian Model With Local Contrast and Consistency Constraint for Small Target Detection

Xia, C., Li, X., Zhao, L., & Yu, S. (2020) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2020.3024642 · Cited by 13

A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication

Andrzej Lingas, B. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-04128-0_37 · Cited by 13

Fast Algorithms for Maximum Subset Matching and All-Pairs Shortest Paths in Graphs with a (Not So) Small Vertex Cover

Alon, N., & Yuster, R. (2007) · Springer eBooks · doi:10.1007/978-3-540-75520-3_17 · Cited by 13

Fast rectangular matrix multiplications and improving parallel matrix computations

Huang, X., & Pan, V. Y. (1997) · Parallel Symbolic Computation · doi:10.1145/266670.266679 · Cited by 13

Reconstruction of graphs based on random walks

Wittmann, D. M., Schmidl, D., Blöchl, F., & Theis, F. J. (2009) · Theoretical Computer Science · doi:10.1016/j.tcs.2009.05.026 · Cited by 13

Recognising k-connected hypergraphs in cubic time

Drewes, F. (1993) · Theoretical Computer Science · doi:10.1016/0304-3975(93)90065-2 · Cited by 13

Mobile Parallel Computing

Doolan, D. C., Tabirca, S., & Yang, L. T. (2006) · International Symposium on Parallel and Distributed Computing · doi:10.1109/ispdc.2006.33 · Cited by 13

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation

Hasani, M. H., Gharibzadeh, S., Farjami, Y., & Tavakkoli, J. (2013) · The Journal of the Acoustical Society of America · doi:10.1121/1.4774278 · Cited by 13

Matrix sparsification and nested dissection over arbitrary fields

Alon, N., & Yuster, R. (2013) · Journal of the ACM · doi:10.1145/2508028.2505989 · Cited by 16

Lower Bounds for Testing Triangle-freeness in Boolean Functions

Bhattacharyya, A., & Xie, N. (2009) · NOT FOUND REPOSITORY (Indian Institute of Science Bangalore) · Cited by 13

Fast Boolean Matrix Multiplication for Highly Clustered Data

Björklund, A., & Andrzej Lingas, B. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44634-6_24 · Cited by 13

Supereffective slow-down of parallel computations

Pan, V. Y., & Preparata, F. P. (1992) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/140901.141926 · Cited by 13

Unique Lowest Common Ancestors in Dags Are Almost as Easy as Matrix Multiplication

Kowaluk, M., & Andrzej Lingas, B. (2007) · Springer eBooks · doi:10.1007/978-3-540-75520-3_25 · Cited by 13

On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity

Bürgisser, P. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44683-4_2 · Cited by 14

A - Lower Bound for the Rank of - Matrix Multiplication over Arbitrary Fields

Bläser, M. (1999) · Cited by 13

Fault identification algorithmic: a new formal approach

Ayeb, B. (2003) · IEEE International Symposium on Fault-Tolerant Computing · doi:10.1109/ftcs.1999.781044 · Cited by 13

Tree-Adjoining Language Parsing in $O(n^6 )$ Time

Rajasekaran, S. (1996) · SIAM Journal on Computing · doi:10.1137/s009753979326009x · Cited by 13

TAL recognition in O(M(n2)) time

Rajasekaran, S., & Yooseph, S. (1995) · Proceedings of the conference - Association for Computational Linguistics. Meeting · doi:10.3115/981658.981681 · Cited by 13

TAL Recognition inO(M(n2)) Time

Rajasekaran, S., & Yooseph, S. (1998) · Journal of Computer and System Sciences · doi:10.1006/jcss.1997.1537 · Cited by 13

Parallel Algorithms for Reducible Flow Graphs

Ramachandran, V. (1997) · Journal of Algorithms · doi:10.1006/jagm.1996.0820 · Cited by 13

Cryptanalysis of LILI-128

Babbage, S. (2001) · Cited by 13

Efficient Dense Gaussian Elimination over the Finite Field with Two ElementsPreprint

Albrecht, M. R., Bard, G. V., & Pernet, C. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1111.6549 · Cited by 13

Efficient parallel algorithms for path problems in planar directed graphs

Andrzej Lingas, B. (1990) · Lecture notes in computer science · doi:10.1007/3-540-52921-7_94 · Cited by 13

Visualization of Non-vectorial Data Using Twin Kernel Embedding

Guo, Y., Gao, J., & Kwan, P. (2006) · doi:10.1109/aidm.2006.18 · Cited by 13

All-pairs small-stretch paths

Cohen, E., & Zwick, U. (1997) · doi:10.5555/314161.314190 · Cited by 13

Chip-Firing Games with Dirichlet Eigenvalues and Discrete Green's Functions

Ellis, R. B., Buss, S. R., Hu, T. C., & Graham, R. L. (2002) · Cited by 13

Learning knowledge to support domain-independent narrative intelligence

Li, B. (2015) · SMARTech Repository (Georgia Institute of Technology) · Cited by 13

Entropy of Operators or why Matrix Multiplication is Hard for Depth-Two Circuits

Jukna, S. P. (2008) · Theory of Computing Systems · doi:10.1007/s00224-008-9133-y · Cited by 12

Accelerating Viterbi algorithm on graphics processing units

Hanif, M. K., & Zimmermann, K.-H. (2017) · Computing · doi:10.1007/s00607-017-0557-6 · Cited by 12

Improving local search in a minimum vertex cover solver for classes of networks

Wagner, M., Friedrich, T., & Lindauer, M. (2017) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2017.7969507 · Cited by 12

BL-ECD

Zhang, J., Cui, L., Yu, P. S., & Lv, Y. (2017) · ACM International Conference on Information and Knowledge Management (CIKM) · doi:10.1145/3132847.3133026 · Cited by 12

SADCMF: Self-Attentive Deep Consistent Matrix Factorization for Micro-Video Multi-Label Classification

Fan, F., Jing, P., Nie, L., Gu, H., & Su, Y. (2024) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2024.3406196 · Cited by 12

New bounds on the classical and quantum communication complexity of some graph properties

Ivanyos, G., Klauck, H., Lee, T., Sántha, M., & de Wolf, R. (2012) · UvA-DARE (University of Amsterdam) · doi:10.4230/lipics.fsttcs.2012.148 · Cited by 12

Approximating Average Parameters of Graphs

Goldreich, O., & Ron, D. (2006) · Lecture notes in computer science · doi:10.1007/11830924_34 · Cited by 12

Estimating Mean First Passage Time of Biased Random Walks with Short Relaxation Time on Complex Networks

Lee, Z. Q., Hsu, W.-J., & Lin, M. (2014) · PLoS ONE · doi:10.1371/journal.pone.0093348 · Cited by 12

Querying parse trees of stochastic context-free grammars

Cohen, S., & Kimelfeld, B. (2010) · International Conference on Database Theory · doi:10.1145/1804669.1804680 · Cited by 12

Computing the rooted triplet distance between galled trees by counting triangles

Jansson, J., & Andrzej Lingas, B. (2013) · Journal of Discrete Algorithms · doi:10.1016/j.jda.2013.10.002 · Cited by 12

Solving toeplitz- and vandermonde-like linear systems with large displacement rank

Bostan, A., Jeannerod, C.-P., & Schost, É. (2007) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1277548.1277554 · Cited by 12

A Study in the Computational Complexity of Temporal Reasoning

Broxvall, M. (2002) · Cited by 12

On the reduction of total‐cost and average‐cost MDPs to discounted MDPs

Feinberg, E. A., & Huang, J. (2017) · Naval Research Logistics (NRL) · doi:10.1002/nav.21743 · Cited by 12

Statistical properties of structured random matrices

Bogomolny, E., & Giraud, O. (2021) · Physical review. E · doi:10.1103/physreve.103.042213 · Cited by 12

Rank and border rank of Kronecker powers of tensors and Strassen's laser method

Conner, A., Gesmundo, F., Landsberg, J. M., & Ventura, E. (2021) · Computational Complexity · doi:10.1007/s00037-021-00217-y · Cited by 18

Randomized Algorithms

Moore, C., & Mertens, S. (2011) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199233212.003.0010 · Cited by 12

All-pairs shortest paths with a sublinear additive error

Roditty, L., & Shapira, A. (2011) · ACM Transactions on Algorithms · doi:10.1145/2000807.2000813 · Cited by 12

Efficient Algorithms for Reconstructing Zero-Recombinant Haplotypes on a Pedigree Based on Fast Elimination of Redundant Linear Equations

Xiao, J., Liu, L., Xia, L., & Jiang, T. (2009) · SIAM Journal on Computing · doi:10.1137/070687591 · Cited by 12

Recognizing quasi-triangulated graphs

Spinrad, J. (2003) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(03)00295-6 · Cited by 12

Restricted Global Grammar Constraints

Katsirelos, G., Maneth, S., Narodytska, N., & Walsh, T. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-04244-7_40 · Cited by 12

Deadlock avoidance in parallel programs with futures: why parallel tasks should not wait for strangers

Cogumbreiro, T., Surendran, R., Martins, F., Sarkar, V., VASCONCELOS, V. T., & Grossman, M. (2017) · Proceedings of the ACM on Programming Languages · doi:10.1145/3143359 · Cited by 12

Unified all-pairs shortest path algorithms in the chordal hierarchy

Han, K., Sekharan, C. N., & Sridhar, R. (1997) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(96)00103-5 · Cited by 12

Black box Frobenius decompositions over small fields

Eberly, W. (2000) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/345542.345596 · Cited by 12

Dynamic matrix rank

Frandsen, G. S., & Frandsen, P. F. (2009) · Theoretical Computer Science · doi:10.1016/j.tcs.2009.06.012 · Cited by 12

Cutting Planes and the Elementary Closure in Fixed Dimension

Bockmayr, A., & Eisenbrand, F. (2001) · Mathematics of Operations Research · doi:10.1287/moor.26.2.304.10555 · Cited by 12

Partitioning Based Algorithms for Some Colouring Problems

Angelsmark, O., & Thapper, J. (2006) · Lecture notes in computer science · doi:10.1007/11754602_4 · Cited by 12

Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system

Li, K., & Pan, V. Y. (2003) · IEEE International Parallel and Distributed Processing Symposium (IPDPS) · doi:10.1109/ipps.1999.760431 · Cited by 12

The Geometry of Constrained Structured Prediction: Applications to Inference and Learning of Natural Language Syntax

Martins, T., & Filipe, A. (2012) · Cited by 12

Field extension and trilinear aggregating, uniting and canceling for the acceleration of matrix multiplications

Pan, V. Y. (1979) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1979.17 · Cited by 43

Trilinear aggregating with implicit canceling for a new acceleration of matrix multiplication

Pan, V. Y. (1982) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(82)90037-2 · Cited by 33

The techniques of trilinear aggregating and the recent progress in the asymptotic acceleration of matrix operations

Pan, V. Y. (1984) · Theoretical Computer Science · doi:10.1016/0304-3975(84)90107-5 · Cited by 4

Fast matrix multiplication without APA-algorithms

Pan, V. Y. (1982) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(82)90029-3 · Cited by 6

Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations

Pan, V. Y. (1978) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1978.34 · Cited by 121