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

Structure Prediction and Computation of Sparse Matrix Products

Cohen, E. (1998) · Journal of Combinatorial Optimization · doi:10.1023/a:1009716300509 · Cited by 46

Efficient Perturbations for Handling Geometric Degeneracies

Emiris, I. Z., Canny, J., & Seidel, R. (1997) · Algorithmica · doi:10.1007/pl00014417 · Cited by 44

Tight lower bounds for certain parameterized NP-hard problems

Chen, J., Chor, B., Fellows, M. R., Huang, X., Juedes, D., Kanj, I. A., & Xia, G. (2004) · IEEE Conference on Computational Complexity (CCC) · doi:10.1109/ccc.2004.1313826 · Cited by 44

Asymptotic entanglement transformation between W and GHZ states

Vrana, P., & Christandl, M. (2015) · Journal of Mathematical Physics · doi:10.1063/1.4908106 · Cited by 52

Enumerating with constant delay the answers to a query

Segoufin, L. (2013) · International Conference on Database Theory · doi:10.1145/2448496.2448498 · Cited by 43

Matrix Representation of Conflict Resolution in Multiple-Decision-Maker Graph Models with Preference Uncertainty

Xu, H., Kilgour, D. M., & Hipel, K. W. (2010) · Group Decision and Negotiation · doi:10.1007/s10726-010-9188-4 · Cited by 43

I/O-Efficient Algorithms on Triangle Listing and Counting

Hu, X., Tao, Y., & Chung, C. (2014) · ACM Transactions on Database Systems · doi:10.1145/2691190.2691193 · Cited by 43

Rotation Invariant Kernels and Their Application to Shape Analysis

Hamsici, O. C., & Martı́nez, A. M. (2008) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.234 · Cited by 43

Topological Persistence for Circle-Valued Maps

Burghelea, D., & Dey, T. K. (2013) · Discrete & Computational Geometry · doi:10.1007/s00454-013-9497-x · Cited by 43

Computational Applications Of Noise Sensitivity

O’Donnell, R. (2018) · KiltHub Repository · doi:10.1184/r1/6604301 · Cited by 43

Cover times, blanket times, and majorizing measures

Ding, J., Lee, J. R., & Peres, Y. (2011) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/1993636.1993646 · Cited by 43

All-Pairs Shortest Paths with Real Weights in O(n 3/log n) Time

Chan, T. M. (2005) · Lecture notes in computer science · doi:10.1007/11534273_28 · Cited by 43

Computing the Fréchet distance between simple polygons in polynomial time

Buchin, K., Buchin, M., & Wenk, C. (2006) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1137856.1137870 · Cited by 43

Variational quantum algorithms for dimensionality reduction and classification

Liang, J., Shen, S., Li, M., & Li, L. (2020) · Physical Review A · doi:10.1103/physreva.101.032323 · Cited by 42

Cache Oblivious Algorithms

Kumar, P. (2003) · Lecture notes in computer science · doi:10.1007/3-540-36574-5_9 · Cited by 43

Computing the rank and a small nullspace basis of a polynomial matrix

Storjohann, A., & Villard, G. (2005) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1073884.1073927 · Cited by 42

Improved dynamic reachability algorithms for directed graphs

Roditty, L., & Zwick, U. (2003) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2002.1181993 · Cited by 42

Answering distance queries in directed graphs using fast matrix multiplication

Yuster, R., & Zwick, U. (2005) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2005.20 · Cited by 42

Fast and Effective Techniques for T-Count Reduction via Spider Nest IdentitiesPreprint

de Beaudrap, N., Bian, X., & Wang, Q. (2020) · arXiv (Cornell University) · doi:10.4230/lipics.tqc.2020.11 · Cited by 66

Annotating Simplices with a Homology Basis and Its Applications

Busaryev, O., Cabello, S., Chen, C., Dey, T. K., & Wang, Y. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-31155-0_17 · Cited by 41

Randomized Preprocessing of Homogeneous Linear Systems of Equations

Pan, V. Y., & Qian, G. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.01.023 · Cited by 41

Weighted Spectral Efficiency Optimization for Hybrid Beamforming in Multiuser Massive MIMO-OFDM Systems

Du, J., Xu, W., Zhao, C., & Vandendorpe, L. (2019) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2019.2932128 · Cited by 41

Dasta – Alternative Linear Layer for Rasta

Hebborn, P., & Leander, G. (2020) · IACR Transactions on Symmetric Cryptology · doi:10.46586/tosc.v2020.i3.46-86 · Cited by 41

On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields

Satoh, T. (2002) · Lecture notes in computer science · doi:10.1007/3-540-45455-1_5 · Cited by 41

Sets of nonnegative matrices without positive products

Protasov, V. Y., & Voynov, A. S. (2012) · Linear Algebra and its Applications · doi:10.1016/j.laa.2012.02.029 · Cited by 41

Efficient Colored Orthogonal Range Counting

Kaplan, H. Y., Rubin, N., Sharir, M., & Verbin, E. (2008) · SIAM Journal on Computing · doi:10.1137/070684483 · Cited by 41

Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

Boyer, B., Dumas, J., Pernet, C., & Zhou, W. (2009) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1576702.1576713 · Cited by 46

Structural control of single-input rank one bilinear systems

Ghosh, S., & Ruths, J. (2015) · Automatica · doi:10.1016/j.automatica.2015.10.053 · Cited by 41

Computing Hermite and Smith normal forms of triangular integer matrices

Storjohann, A. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10012-5 · Cited by 41

Faster Clustering Coefficient Using Vertex Covers

Green, O., & Bader, D. A. (2013) · International Conference on Social Computing · doi:10.1109/socialcom.2013.51 · Cited by 40

Modeling cooperation in multi-agent communities

Buccafurri, F., Rosaci, D., Sarnè, G. M. L., & Palopoli, L. (2004) · Cognitive Systems Research · doi:10.1016/j.cogsys.2004.03.001 · Cited by 42

Empathetic social choice on social networks

Salehi‐Abari, A., & Boutilier, C. E. (2014) · doi:10.5555/2615731.2615843 · Cited by 40

The growth rate of tri-colored sum-free sets

Kleinberg, R., Sawin, W., & Speyer, D. E. (2018) · Discrete Analysis · doi:10.19086/da.3734 · Cited by 40

A Strongly Polynomial Algorithm for a Class of Minimum-Cost Flow Problems with Separable Convex Objectives

Végh, L. A. (2016) · SIAM Journal on Computing · doi:10.1137/140978296 · Cited by 40

Partial Derivatives in Arithmetic Complexity and Beyond

Chen, X., Kayal, N., & Wigderson, A. (2011) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000043 · Cited by 49

Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Lifshits, Y., Mozes, S., Weimann, O., & Ziv-Ukelson, M. (2007) · Algorithmica · doi:10.1007/s00453-007-9128-0 · Cited by 41

Four proofs for the Cheeger inequality and graph partition algorithms

Chung, F. (2007) · Cited by 40

An O ( n 3 ) algorithm for the Frobenius normal form

Storjohann, A. (1998) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/281508.281570 · Cited by 40

A practical algorithm for faster matrix multiplication

Kaporin, I. (1999) · Numerical Linear Algebra with Applications · doi:10.1002/(sici)1099-1506(199912)6:8 · Cited by 41

Processor-efficient parallel solution of linear systems. II. The positive characteristic and singular cases

Kaltofen, E., & Pan, V. Y. (1992) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1992.267779 · Cited by 40

Checking approximate computations over the reals

Ar, S., Blum, M., Codenotti, B., & Gemmell, P. S. (1993) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/167088.167288 · Cited by 40

Runtime guarantees for regression problems

Chin, H. H., Mądry, A., Miller, G. L., & Peng, R. (2013) · Conference on Innovations in Theoretical Computer Science · doi:10.1145/2422436.2422469 · Cited by 42

Flexible Affinity Matrix Learning for Unsupervised and Semisupervised Classification

Fang, X., Han, N., Wong, W. K., Teng, S., Wu, J., Xie, S., & Li, X. (2018) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2018.2861839 · Cited by 39

Abelian tensors

Landsberg, J. M., & Michałek, M. (2016) · Journal de Mathématiques Pures et Appliquées · doi:10.1016/j.matpur.2016.11.004 · Cited by 39

Counting and Detecting Small Subgraphs via Equations

Kowaluk, M., Andrzej Lingas, B., & Lundell, E.-M. (2013) · SIAM Journal on Discrete Mathematics · doi:10.1137/110859798 · Cited by 39

Faster inversion and other black box matrix computations using efficient block projections

Eberly, W., Giesbrecht, M. W., Pascal Giorgi, A., Storjohann, A., & Villard, G. (2007) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1277548.1277569 · Cited by 39

An $\tilde{O}(m^{2}n)$ Algorithm for Minimum Cycle Basis of Graphs

Kavitha, T., Mehlhorn, K., Michail, D., & Paluch, K. E. (2007) · Algorithmica · doi:10.1007/s00453-007-9064-z · Cited by 39

Computing stabilized norms for quantum operations

Johnston, N., Kribs, D. W., & Paulsen, V. I. (2009) · Quantum Information and Computation · doi:10.26421/qic9.1-2-2 · Cited by 39

Counting curves and their projections

Gathen, J. V. Z., Karpiński, M., & Shparlinski, I. E. (1996) · Computational Complexity · doi:10.1007/bf01202042 · Cited by 40

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

Li, K., & Pan, V. Y. (2001) · IEEE Transactions on Computers · doi:10.1109/12.926164 · Cited by 39

Statistical cryptanalysis of block ciphers

Junod, P. (2005) · reroDoc Digital Library · doi:10.5075/epfl-thesis-3179 · Cited by 39

Partial Derivatives in Arithmetic Complexity and Beyond

Chen, X. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984814 · Cited by 38

Robust Transceiver Optimization for Downlink Coordinated Base Station Systems: Distributed Algorithm

Bogale, T. E., Vandendorpe, L., & Chalise, B. K. (2011) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2011.2170167 · Cited by 38

Multimodal Learning toward Micro-Video Understanding

Nie, L., Liu, M., & Song, X. (2019) · Synthesis lectures on image, video, and multimedia processing · doi:10.2200/s00938ed1v01y201907ivm020 · Cited by 38

Quantum support vector machine based on regularized Newton method

Zhang, R., Wang, J., Jiang, N., Li, H., & Wang, Z. (2022) · Neural Networks · doi:10.1016/j.neunet.2022.03.043 · Cited by 40

Variational quantum approximate support vector machine with inference transfer

Park, S., Park, D. K., & Rhee, J. K. (2023) · Scientific Reports · doi:10.1038/s41598-023-29495-y · Cited by 40

Optimization techniques for small matrix multiplication

Drevet, C. É., Islam, M. N., & Schost, É. (2010) · Theoretical Computer Science · doi:10.1016/j.tcs.2010.12.012 · Cited by 43

Using Selective Path-Doubling for Parallel Shortest-Path Computations

Cohen, E. (1997) · Journal of Algorithms · doi:10.1006/jagm.1996.0813 · Cited by 38

Even-hole-free graphs: A survey

Vušković, K. (2010) · Applicable Analysis and Discrete Mathematics · doi:10.2298/aadm100812027v · Cited by 38

Statistical Thermal Profile Considering Process Variations: Analysis and Applications

Jaffari, J., & Anis, M. H. (2008) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2008.923251 · Cited by 38

An output-sensitive algorithm for persistent homology

Chen, C., & Kerber, M. (2012) · Computational Geometry · doi:10.1016/j.comgeo.2012.02.010 · Cited by 38

Maximum Matchings in Planar Graphs via Gaussian Elimination

Mucha, M., & Sankowski, P. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-30140-0_48 · Cited by 38

Algorithms and resource requirements for fundamental problems

Blum, M., & Williams, R. (2007) · Cited by 38

Optimization of Block Size for CBFM in MoM

Konno, K., Chen, Q., Sawaya, K., & Sezai, T. (2012) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2012.2207330 · Cited by 37

Multi-modal constraint propagation for heterogeneous image clustering

Fu, Z., Ip, H. H. S., Lu, H., & Lu, Z. (2011) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/2072298.2072318 · Cited by 37

Dynamic shortest paths and transitive closure: Algorithmic techniques and data structures

Demetrescu, C., & Italiano, G. F. (2006) · Journal of Discrete Algorithms · doi:10.1016/j.jda.2005.12.003 · Cited by 37

On Low Tree-Depth Decompositions

Nešetřil, J., & de Mendez, P. O. (2015) · Graphs and Combinatorics · doi:10.1007/s00373-015-1569-7 · Cited by 37

Finding a long directed cycle

Gabow, H. N., & Nie, S. (2008) · ACM Transactions on Algorithms · doi:10.1145/1328911.1328918 · Cited by 37

Fast Discrete Fourier Spectra Attacks on Stream Ciphers

Gong, G., Rønjom, S., Helleseth, T., & Hu, H. (2011) · IEEE Transactions on Information Theory · doi:10.1109/tit.2011.2158480 · Cited by 37

Adaptive Graph Guided Embedding for Multi-label Annotation

Wang, L., Ding, Z., & Fu, Y. (2018) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2018/388 · Cited by 37

An Improved Construction of Progression-Free Sets

Elkin, M. (2010) · ACM-SIAM Symposium on Discrete Algorithms (SODA) · doi:10.1137/1.9781611973075.72 · Cited by 37

Fully dynamic all pairs shortest paths with real edge weights

Demetrescu, C., & Italiano, G. F. (2001) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2001.959900 · Cited by 37

Graph expansion and communication costs of fast matrix multiplication

Ballard, G., Demmel, J. W., Holtz, O., & Schwartz, O. (2011) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/1989493.1989495 · Cited by 37

Arboricity, h -index, and dynamic algorithms

Lin, M. C., Soulignac, F. J., & SZWARCFITER, J. L. (2011) · Theoretical Computer Science · doi:10.1016/j.tcs.2011.12.006 · Cited by 36

Testing 2-Vertex Connectivity and Computing Pairs of Vertex-Disjoint s-t Paths in Digraphs

Georgiadis, L. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-14165-2_62 · Cited by 36

A local approach to concept generation

Berry, A., Bordat, J.-P., & Sigayret, A. (2007) · Annals of Mathematics and Artificial Intelligence · doi:10.1007/s10472-007-9063-4 · Cited by 36

Fast Algorithms for Linear Algebra Modulo N

Storjohann, A., & Mulders, T. (1998) · Lecture notes in computer science · doi:10.1007/3-540-68530-8_12 · Cited by 36

Constant Delay Enumeration for Conjunctive Queries

Segoufin, L. (2015) · ACM SIGMOD Record · doi:10.1145/2783888.2783894 · Cited by 36

A Novel Transmitter-Based Selective-Precoding Technique for DS/CDMA Systems

Masouros, C., & Alsusa, E. A. (2007) · IEEE Signal Processing Letters · doi:10.1109/lsp.2007.896196 · Cited by 36

Point algebras for temporal reasoning: Algorithms and complexity

Broxvall, M., & Jönsson, P. (2003) · Artificial Intelligence · doi:10.1016/s0004-3702(03)00075-4 · Cited by 36

Newton’s method and FFT trading

van der Hoeven, J. (2010) · Journal of Symbolic Computation · doi:10.1016/j.jsc.2010.03.005 · Cited by 37

Efficient parallel algorithms for optical computing with the discrete Fourier transform (DFT) primitive

Reif, J. H., & Tyagi, A. K. (1997) · Applied Optics · doi:10.1364/ao.36.007327 · Cited by 36

Estimating the size of the transitive closure in linear time

Cohen, E. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365694 · Cited by 36

On Vaidya's Volumetric Cutting Plane Method for Convex Programming

Anstreicher, K. M. (1997) · Mathematics of Operations Research · doi:10.1287/moor.22.1.63 · Cited by 36

Parsing by matrix multiplication generalized to Boolean grammars

Okhotin, A. (2013) · Theoretical Computer Science · doi:10.1016/j.tcs.2013.09.011 · Cited by 36

Fast operations on linearized polynomials and their applications in coding theory

Puchinger, S., & Wachter-Zeh, A. (2017) · Journal of Symbolic Computation · doi:10.1016/j.jsc.2017.11.012 · Cited by 38

Modified Differential Evolution with Locality induced Genetic Operators for dynamic optimization

Mukherjee, R., Debchoudhury, S., & Das, S. (2016) · European Journal of Operational Research · doi:10.1016/j.ejor.2016.02.042 · Cited by 35

Breaking the FF3 Format-Preserving Encryption Standard over Small Domains

Durak, F. B., & Serge Vaudenay, B. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-63715-0_23 · Cited by 35

Algebraic secret sharing using privacy homomorphisms for IoT-basedhealthcare systems

Chang, C.-C., & Li, C. (2019) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2019168 · Cited by 36

Comparing alternatives to the fixed degree sequence model for extracting the backbone of bipartite projections

Neal, Z. P., Domagalski, R., & Sagan, B. E. (2021) · Scientific Reports · doi:10.1038/s41598-021-03238-3 · Cited by 35

Splitting Randomized Stationary Policies in Total-Reward Markov Decision Processes

Feinberg, E. A., & Rothblum, U. G. (2012) · Mathematics of Operations Research · doi:10.1287/moor.1110.0525 · Cited by 36

Expressivity and Complexity of the Grammatical Framework

Ljunglöf, P. (2004) · Cited by 35

Finding heaviest H -subgraphs in real weighted graphs, with applications

Williams, V. V., Williams, R., & Yuster, R. (2010) · ACM Transactions on Algorithms · doi:10.1145/1798596.1798597 · Cited by 35

Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives

Végh, L. A. (2012) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/2213977.2213981 · Cited by 35

The Exact Path Length Problem

Nykänen, M., & Ukkonen, E. (2002) · Journal of Algorithms · doi:10.1006/jagm.2001.1201 · Cited by 35

On the Security of a Cryptosystem Based on Multiple-Parameters Discrete Fractional Fourier Transform

Youssef, A. (2008) · IEEE Signal Processing Letters · doi:10.1109/lsp.2007.910299 · Cited by 35

Fast algorithms for the Sylvester equation AX−XBT=C

Kirrinnis, P. (2001) · Theoretical Computer Science · doi:10.1016/s0304-3975(00)00322-4 · Cited by 36

Fast Fourier analysis for abelian group extensions

Rockmore, D. N. (1990) · Advances in Applied Mathematics · doi:10.1016/0196-8858(90)90008-m · Cited by 35

Vertex splitting and the recognition of trapezoid graphs

Mertzios, G. B., & Corneil, D. G. (2011) · Discrete Applied Mathematics · doi:10.1016/j.dam.2011.03.023 · Cited by 34

All-Pairs Shortest Paths Computation in the BSP Model

Tiskin, A. (2001) · Lecture notes in computer science · doi:10.1007/3-540-48224-5_15 · Cited by 34

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