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

(1984) · Lecture notes in computer science · doi:10.1007/3-540-13866-8 · Cited by 147

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

3 1 On Rational-Interpolation Based List-Decoding and List-Decoding Binary Goppa CodesPreprint

Beelen, P., Høholdt, T., Rosenkilde, J., Wu, Y., & Member, S. (2013) · Cited by 18

Subcubic certificates for CFL reachability

Chistikov, D. V., Majumdar, R., & Schepper, P. (2022) · Proceedings of the ACM on Programming Languages · doi:10.1145/3498702 · Cited by 23

Filter-function formalism and software package to compute quantum processes of gate sequences for classical non-Markovian noise

Hangleiter, T., Cerfontaine, P., & Bluhm, H. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043047 · Cited by 21

Learning Dual Low-Rank Representation for Multi-Label Micro-Video Classification

Lu, W. D., Li, D., Nie, L., Jing, P., & Su, Y. (2021) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2021.3121567 · Cited by 17

Successive Linear Approximation VBI for Joint Sparse Signal Recovery and Dynamic Grid Parameters Estimation

Xu, W., Liu, A., Zhou, B., & Zhao, M. (2025) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2025.3574489 · Cited by 17

Computing Shortest Paths in 2D and 3D Memristive Networks

Ye, Z., Wu, S. H. M., & Prodromakis, T. (2013) · Springer eBooks · doi:10.1007/978-3-319-02630-5_24 · Cited by 17

On the exact and approximate bilinear complexities of multiplication of 4×2 and 2×2 matrices

Alekseev, V. B., & Smirnov, A. V. (2013) · Proceedings of the Steklov Institute of Mathematics · doi:10.1134/s0081543813070079 · Cited by 17

A fast algorithm for computing the characteristic polynomial of the p-curvature

Bostan, A., Caruso, X., & Schost, É. (2014) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/2608628.2608650 · Cited by 17

Finding and listing induced paths and cycles

Hoàng, C. T., Kamiński, M., Sawada, J., & Sritharan, R. (2012) · Discrete Applied Mathematics · doi:10.1016/j.dam.2012.01.024 · Cited by 17

Finding associations and computing similarity via biased pair sampling

Campagna, A., & Pagh, R. (2011) · Knowledge and Information Systems · doi:10.1007/s10115-011-0428-y · Cited by 17

Work-Preserving Speed-Up of Parallel Matrix Computations

Pan, V. Y., & Preparata, F. P. (1995) · SIAM Journal on Computing · doi:10.1137/0224051 · Cited by 17

Algorithms for Simultaneous Padé Approximations

Rosenkilde, J., & Storjohann, A. (2016) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/2930889.2930933 · Cited by 17

Exact and Approximation Algorithms for Weighted Matroid Intersection

Huang, C.-C., Kakimura, N., & Kamiyama, N. (2015) · Mathematical Programming · doi:10.1007/s10107-018-1260-x · Cited by 17

Sensing-Constrained LQG Control

Tzoumas, V., Carlone, L., Pappas, G. J., & Jadbabaie, A. (2018) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2018.8431439 · Cited by 17

A Partial Differential Equation Approach to Inhalation Physiologically Based Pharmacokinetic Modeling

Boger, E., & Wigström, O. (2018) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.12344 · Cited by 17

Faster Matrix Multiplication via Sparse Decomposition

Beniamini, G., & Schwartz, O. (2019) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/3323165.3323188 · Cited by 22

Improving connectivity of compromised digital networks via algebraic connectivity maximisation

Cheung, K.-F., & Bell, M. G. H. (2021) · European Journal of Operational Research · doi:10.1016/j.ejor.2021.01.015 · Cited by 17

Dynamic Matchings in Convex Bipartite Graphs

Brodal, G. S., Georgiadis, L., Hansen, K. A., & Katriel, I. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-74456-6_37 · Cited by 17

Nilpotent adjacency matrices, random graphs and quantum random variables

Schott, R., & Staples, G. S. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/15/155205 · Cited by 17

On sparse representations of linear operators and the approximation of matrix products

Belabbas, M.-A., & Wolfe, P. J. (2008) · Conference on Information Sciences and Systems · doi:10.1109/ciss.2008.4558532 · Cited by 17

Finding and counting cliques and independent sets in r-uniform hypergraphs

Yuster, R. (2006) · Information Processing Letters · doi:10.1016/j.ipl.2006.04.005 · Cited by 17

On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation

Strozecki, Y. (2013) · Theory of Computing Systems · doi:10.1007/s00224-012-9442-z · Cited by 17

Weighted isotonic regression under the L1 norm

Angelov, S., Harb, B., Kannan, S., & Wang, L. (2006) · doi:10.5555/1109557.1109643 · Cited by 17

A shortest cycle for each vertex of a graph

Yuster, R. (2011) · Information Processing Letters · doi:10.1016/j.ipl.2011.07.019 · Cited by 17

A Kalman-Based Coordination for Hierarchical State Estimation: Agorithm and Analysis

Zonouz, S., & Sanders, W. H. (2008) · Hawaii International Conference on System Sciences (HICSS) · doi:10.1109/hicss.2008.23 · Cited by 17

Bulk-Synchronous Parallel Gaussian Elimination

Tiskin, A. (2002) · Journal of Mathematical Sciences · doi:10.1023/a:1013588221172 · Cited by 17

A glimpse on constant delay enumeration (Invited Talk)

Segoufin, L. (2014) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.stacs.2014.13 · Cited by 17

Approximating Cycles in Directed Graphs: Fast Algorithms for Girth and Roundtrip Spanners

Pachocki, J., Roditty, L., Sidford, A., Tov, R., & Williams, V. V. (2018) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611975031.91 · Cited by 17

A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs

Kavitha, T., & Mehlhorn, K. (2005) · Lecture notes in computer science · doi:10.1007/978-3-540-31856-9_54 · Cited by 17

Linear-Processor NC Algorithms for Planar Directed Graphs I: Strongly Connected Components

Kao, M. (1993) · SIAM Journal on Computing · doi:10.1137/0222032 · Cited by 17

Attacks based on Conditional Correlations against the Nonlinear Filter Generator.

Löhlein, B. (2003) · Cited by 17

Degree-preserving trees

Broersma, H. J., Koppius, O., Tuinstra, H., Huck, A., Kloks, T., Kratsch, D., & M�ller, H. (2000) · Networks · doi:10.1002/(sici)1097-0037(200001)35:1 · Cited by 17

A framework for cost-scaling algorithms for submodular flow problems

Gabow, H. N. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1993.366842 · Cited by 17

Which groups are amenable to proving exponent two for matrix multiplication?Preprint

Blasiak, J., Church, T., Cohn, H., Grochow, J. A., & Umans, C. (2017) · arXiv (Cornell University) · doi:10.4230/lipics.ccc.2025.9 · Cited by 17

New applications of the polynomial method: The cap set conjecture and beyond

Grochow, J. (2018) · Bulletin of the American Mathematical Society · doi:10.1090/bull/1648 · Cited by 16

A sub-cubic time algorithm for computing the quartet distance between two general trees

Nielsen, J., Kristensen, A. K., Mailund, T., & Pedersen, C. N. (2011) · Algorithms for Molecular Biology · doi:10.1186/1748-7188-6-15 · Cited by 16

Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization

Pan, V. Y. (2011) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2011.06.006 · Cited by 16

Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function

Scott, A., & Sorkin, G. B. (2009) · ACM Transactions on Algorithms · doi:10.1145/1597036.1597049 · Cited by 16

A Local Graph Partitioning Algorithm Using Heat Kernel Pagerank

Chung, F. (2009) · Lecture notes in computer science · doi:10.1007/978-3-540-95995-3_6 · Cited by 16

A tight bound for Green's arithmetic triangle removal lemma in vector spaces

Fox, J., & Lovász, L. (2017) · ACM-SIAM Symposium on Discrete Algorithms (SODA) · doi:10.1137/1.9781611974782.106 · Cited by 16

A Novel Underdetermined Source Recovery Algorithm Based on k-Sparse Component Analysis

Eqlimi, E., Makkiabadi, B., Samadzadehaghdam, N., Khajehpour, H., Mohagheghian, F., & Sanei, S. (2018) · Circuits Systems and Signal Processing · doi:10.1007/s00034-018-0910-9 · Cited by 16

Towards a geometric approach to Strassen’s asymptotic rank conjecture

Conner, A., Gesmundo, F., Landsberg, J. M., Ventura, E., & Wang, Y. (2020) · Collectanea mathematica · doi:10.1007/s13348-020-00280-8 · Cited by 22

A Segregated Approach for Modeling the Electrochemistry in the 3-D Microstructure of Li-Ion Batteries and Its Acceleration Using Block Preconditioners

Allen, J. M., Chang, J., Usseglio‐Viretta, F. L. E., Graf, P. A., & Smith, K. A. (2021) · Journal of Scientific Computing · doi:10.1007/s10915-021-01410-5 · Cited by 21

Complex event forecasting with prediction suffix trees

Alevizos, E., Artikis, A., & Παλιούρας, Γ. (2021) · The VLDB Journal · doi:10.1007/s00778-021-00698-x · Cited by 16

Complexity of Algorithms for Linear Systems of Equations

Pan, V. Y. (1991) · Springer eBooks · doi:10.1007/978-3-642-76717-3_2 · Cited by 16

Improved Algorithms for Max-restricted Path Consistency

Grandoni, F., & Italiano, G. F. (2003) · Lecture notes in computer science · doi:10.1007/978-3-540-45193-8_67 · Cited by 16

Novel scheduling strategy for downlink multiuser MIMO system: Particle swarm optimization

Hei, Y., Li, X., Yi, K., & Yang, H. (2009) · Science in China Series F Information Sciences · doi:10.1007/s11432-009-0212-8 · Cited by 16

All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time

Baswana, S., Goyal, V., & Sen, S. (2008) · Theoretical Computer Science · doi:10.1016/j.tcs.2008.10.018 · Cited by 21

Relationless Completeness and Separations

Hrubeš, P., Wigderson, A., & Yehudayoff, A. (2010) · IEEE Conference on Computational Complexity (CCC) · doi:10.1109/ccc.2010.34 · Cited by 16

All-Pairs Bottleneck Paths in Vertex Weighted Graphs

Shapira, A., Yuster, R., & Zwick, U. (2009) · Algorithmica · doi:10.1007/s00453-009-9328-x · Cited by 16

Small Grid Embeddings of 3-Polytopes

Mor, A. R., Rote, G., & Schulz, A. (2010) · Discrete & Computational Geometry · doi:10.1007/s00454-010-9301-0 · Cited by 16

Exact Algorithms for Hard Graph Problems

Grandoni, F. (2004) · Cited by 16

Minimizing the complexity of an activity network

Kamburowski, J., Michael, D. J., & Stallmann, M. F. M. (2000) · Networks · doi:10.1002/1097-0037(200008)36:1 · Cited by 16

Locating service centers with precedence constraints

Kaufman, Y., & Tamir, A. (1993) · Discrete Applied Mathematics · doi:10.1016/0166-218x(93)90130-g · Cited by 16

A recognition algorithm for orders of interval dimension two

Langley, L. J. (1995) · Discrete Applied Mathematics · doi:10.1016/0166-218x(94)00056-j · Cited by 16

On Dynamic Algorithms for Algebraic Problems

Reif, J. H., & Tate, S. R. (1997) · Journal of Algorithms · doi:10.1006/jagm.1995.0807 · Cited by 18

Geometric algorithms for the minimum cost assignment problem

Tokuyama, T., & Nakano, J. (1995) · Random Structures and Algorithms · doi:10.1002/rsa.3240060403 · Cited by 16

Dynamic subgraph connectivity with geometric applications

Chan, T. M. (2002) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/509907.509911 · Cited by 16

An output-sensitive variant of the baby steps/giant steps determinant algorithm

Kaltofen, E. (2002) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/780506.780524 · Cited by 16

Number-Theoretic Algorithms

Bach, E. (1990) · Annual Review of Computer Science · doi:10.1146/annurev.cs.04.060190.001003 · Cited by 16

On certificates and lookahead in dynamic graph problems

Khanna, S., Motwani, R., & Wilson, R. H. (1996) · doi:10.5555/313852.314067 · Cited by 16

From graphs to matrices, and back: new techniques for graph algorithms

Goemans, M. X., Kelner, J. A., & Mądry, A. (2011) · Cited by 16

A New General-Purpose Method to Multiply 3x3 Matrices Using Only 23 MultiplicationsPreprint

Courtois, N. T., Bard, G. V., & Hulme, D. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1108.2830 · Cited by 28

Design and Analysis of Network Codes

Jaggi, S. (2006) · CaltechTHESIS (California Institute of Technology) · doi:10.7907/7erz-h253 · Cited by 16

Deterministic Combinatorial Replacement Paths and Distance Sensitivity OraclesPreprint

Alon, N., Chechik, S., & Cohen, S. (2019) · arXiv (Cornell University) · doi:10.4230/lipics.icalp.2019.12 · Cited by 16

Latency-Aware Multi-Antenna SWIPT System With Battery-Constrained Receivers

Kumar, D., López, O. L. A., Joshi, S. K., & Tölli, A. (2022) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2022.3215864 · Cited by 15

Challenges and Opportunities in the Co-design of Convolutions and RISC-V Vector Processors

Gupta, S. R., Παπαδοπούλου, Ν., & Pericàs, M. (2023) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3624062.3624232 · Cited by 15

Counting k‐component forests of a graph

Myrvold, W. J. (1992) · Networks · doi:10.1002/net.3230220704 · Cited by 17

Fast field solver for the simulation of large-area OLEDs

Pohl, L., Kohári, Z., & Székely, V. (2010) · Microelectronics Journal · doi:10.1016/j.mejo.2009.12.007 · Cited by 15

Clustering via matrix powering

Zhou, H., & Woodruff, D. P. (2004) · ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS) · doi:10.1145/1055558.1055579 · Cited by 15

An output-sensitive algorithm for persistent homology

Chen, C., & Kerber, M. (2011) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1998196.1998228 · Cited by 15

RANDOM NEURAL NETWORK MODEL FOR SUPERVISED LEARNING PROBLEMS : TUTORIAL

Basterrech, S., & Rubino, G. (2015) · Neural Network World · doi:10.48550/arxiv.1609.04846 · Cited by 15

Computing Canonical Bases of Modules of Univariate Relations

Neiger, V., & Xuan, V. T. (2017) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/3087604.3087656 · Cited by 15

On analyzing and evaluating privacy measures for social networks under active attack

DasGupta, B., Mobasheri, N., & Yero, I. G. (2018) · Information Sciences · doi:10.1016/j.ins.2018.09.023 · Cited by 15

Powers of Asteroidal Triple-free Graphs with Applications.

Chang, J., Ho, C.-W., & Ko, M. (2003) · Cited by 15

Efficient sequential and parallel algorithms for planar minimum cost flow

Imai, H., & Iwano, K. (1990) · Lecture notes in computer science · doi:10.1007/3-540-52921-7_52 · Cited by 15

Efficient decomposition of associative algebras

Eberly, W., & Giesbrecht, M. W. (1996) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/236869.236931 · Cited by 15

Fast randomized algorithms for the structure of matrix algebras over finite fields (extended abstract)

Ivanyos, G. (2000) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/345542.345620 · Cited by 15

On Certificates and Lookahead in Dynamic Graph Problems

Khanna, S., Motwani, R., & Wilson, R. H. (1998) · Algorithmica · doi:10.1007/pl00009220 · Cited by 15

Taking roots over high extensions of finite fields

Doliskani, J., & Schost, É. (2013) · Mathematics of Computation · doi:10.1090/s0025-5718-2013-02715-9 · Cited by 15

k-Subgraph Isomorphism on AC_0 Circuits

Amano, K. (2009) · IEEE Conference on Computational Complexity (CCC) · doi:10.1109/ccc.2009.23 · Cited by 15

Rare category analysis

Carbonell, J., & He, J. (2010) · Cited by 15

Analytic Filter-Function Derivatives for Quantum Optimal Control

Le, I. N. M., Teske, J. D., Hangleiter, T., Cerfontaine, P., & Bluhm, H. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.024006 · Cited by 15

Faster multi-witnesses for Boolean matrix multiplication

Gąsieniec, L. A., Kowaluk, M., & Andrzej Lingas, B. (2008) · Information Processing Letters · doi:10.1016/j.ipl.2008.10.012 · Cited by 15

Fast algorithms for differential equations in positive characteristic

Bostan, A., & Schost, É. (2009) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1576702.1576712 · Cited by 15

Finding large 3-free sets I: The small n case

Gasarch, W. I., Glenn, J. R., & Kruskal, C. P. (2007) · Journal of Computer and System Sciences · doi:10.1016/j.jcss.2007.06.002 · Cited by 15

Approximate Max-Flow on Small Depth Networks

Cohen, E. (1995) · SIAM Journal on Computing · doi:10.1137/s0097539792236717 · Cited by 15

Improved Bounds and New Trade-Offs for Dynamic All Pairs Shortest Paths

Demetrescu, C., & Italiano, G. F. (2002) · Lecture notes in computer science · doi:10.1007/3-540-45465-9_54 · Cited by 15

Hammock-on-ears decomposition: A technique for the efficient parallel solution of shortest paths and other problems

Kavvadias, D. J., Pantziou, G. E., Spirakis, P. G., & Zaroliagis, C. (1996) · Theoretical Computer Science · doi:10.1016/s0304-3975(96)00065-5 · Cited by 15

Quantum and Classical Communication-Space Tradeoffs from Rectangle Bounds

Klauck, H. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-30538-5_32 · Cited by 15

Null space and eigenspace computations with additive preprocessing

Pan, V. Y., & Yan, X. (2007) · Symbolic Numeric Computation · doi:10.1145/1277500.1277523 · Cited by 15

Probabilistic algorithm for finding roots of linearized polynomials

Skachek, V., & Roth, R. M. (2007) · Designs Codes and Cryptography · doi:10.1007/s10623-007-9125-y · Cited by 15

Nine Open Problems on Conjunctive and Boolean Grammars.

Okhotin, A. (2007) · Bulletin of the European Association for Theoretical Computer Science · Cited by 15

Fractal Matrix Multiplication: A Case Study on Portability of Cache Performance

Bilardi, G., D’Alberto, P., & Nicolau, A. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44688-5_3 · Cited by 15

Counting curves and their projections

Gathen, J. V. Z., Karpiński, M., & Shparlinski, I. E. (1993) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/167088.167292 · Cited by 15

How to Fake Multiply by a Gaussian MatrixPreprint

Kapralov, M., Potluru, V. K., & Woodruff, D. P. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1606.05732 · Cited by 15

Multithreading and Strassen’s algorithms in SUNRED field solver

Pohl, L. (2008) · International Workshop on Thermal Investigations of ICs and Systems · doi:10.1109/therminic.2008.4669895 · Cited by 14

The clustering of dark sirens' invisible host galaxies

Dalang, C., & Baker, T. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/02/024 · Cited by 14

Graph convolutional networks for spatial interpolation of correlated data

Njifon, M. A., & Schuhmacher, D. (2024) · Spatial Statistics · doi:10.1016/j.spasta.2024.100822 · Cited by 14

Improving Time Bounded Reachability Computations in Interactive Markov Chains

Hatefi, H., & Hermanns, H. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-40213-5_16 · Cited by 14

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