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

Mantaining Dynamic Matrices for Fully Dynamic Transitive Closure

Demetrescu, C., & Italiano, G. F. (2007) · Algorithmica · doi:10.1007/s00453-007-9051-4 · Cited by 21

A framework of filtering, clustering and dynamic layout graphs for visualization

Huang, X., Eades, P., & Lai, W. (2005) · Swinburne figshare (Swinburne University of Technology) · Cited by 21

Large margin vs. large volume in transductive learning

El‐Yaniv, R., Pechyony, D., & Vapnik, V. N. (2008) · Machine Learning · doi:10.1007/s10994-008-5071-9 · Cited by 21

TREE DECOMPOSITIONS OF GRAPHS

Niedermeier, R. (2006) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198566076.003.0010 · Cited by 21

The application of modified Chebyshev polynomials in asymmetric cryptography

Lawnik, M., & Kapczyński, A. (2019) · Computer Science · doi:10.7494/csci.2019.20.3.3307 · Cited by 21

Algorithms for matrix groups

O’Brien, E. A. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511842474.002 · Cited by 22

Reductions in Computational Complexity Using Clifford Algebras

Schott, R., & Staples, G. S. (2008) · Advances in Applied Clifford Algebras · doi:10.1007/s00006-008-0143-2 · Cited by 21

Fast matrix multiplication using coherent configurations

Cohn, H., & Umans, C. (2013) · ACM-SIAM Symposium on Discrete Algorithms (SODA) · doi:10.1137/1.9781611973105.77 · Cited by 31

A note on square roots in finite fields

Bach, E. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.59955 · Cited by 21

Parallel Matrix Computations Using a Reconfigurable Pipelined Optical Bus

Li, K., Pan, Y., & Zheng, S. Q. (1999) · Journal of Parallel and Distributed Computing · doi:10.1006/jpdc.1999.1569 · Cited by 21

Mixed-approach algorithms for transitive closure (extended abstract)

Jakobsson, H. (1991) · ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS) · doi:10.1145/113413.113431 · Cited by 21

Exact Exponential-Time Algorithms for Domination Problems in Graphs

van Rooij, J. M. M. (2011) · Utrecht University Repository (Utrecht University) · Cited by 21

A multi-hop routing protocol based on link state prediction for intra-body Wireless Nanosensor Networks

Xu, J., Zhang, Y., Jiang, J., & Kan, J. (2021) · Ad Hoc Networks · doi:10.1016/j.adhoc.2021.102470 · Cited by 20

Computationally efficient MUSIC based DOA estimation algorithm for FMCW radar

Karim, B. A., & Ali, H. K. (2023) · Journal of Electronic Science and Technology · doi:10.1016/j.jnlest.2023.100192 · Cited by 20

A Structure-Preserving, Upwind-SAV Scheme for the Degenerate Cahn–Hilliard Equation with Applications to Simulating Surface Diffusion

Huang, Q.-A., Jiang, W., Yang, J. Z., & Yuan, C. (2023) · Journal of Scientific Computing · doi:10.1007/s10915-023-02380-6 · Cited by 21

Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Mozes, S., Weimann, O., & Ziv-Ukelson, M. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-73437-6_4 · Cited by 20

Fast and Simple Approximation of the Diameter and Radius of a Graph

Boitmanis, K., Freivalds, K., Lediņš, P., & Opmanis, R. (2006) · Lecture notes in computer science · doi:10.1007/11764298_9 · Cited by 20

Context-Sensitive Probabilistic Boolean Networks: Steady-State Properties, Reduction, and Steady-State Approximation

Pal, R. (2009) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2009.2030832 · Cited by 20

General spanning trees and reachability query evaluation

Chen, Y. (2009) · International C* Conference on Computer Science & Software Engineering · doi:10.1145/1557626.1557665 · Cited by 20

Dynamic compressive spectrum sensing for cognitive radio networks

Yin, W., Wen, Z., Li, S., Meng, J., & Han, Z. (2011) · Conference on Information Sciences and Systems · doi:10.1109/ciss.2011.5766198 · Cited by 20

Tensor decomposition and homotopy continuation

Bernardi, A., Daleo, N. S., Hauenstein, J. D., & Bernard Mourrain, C. (2017) · Differential Geometry and its Applications · doi:10.1016/j.difgeo.2017.07.009 · Cited by 20

Open Set Domain Adaptation via Joint Alignment and Category Separation

Liu, J., Jing, M., Li, J., Lü, K., & Shen, H. T. (2021) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2021.3134673 · Cited by 20

Minimal fill in O ( n 2.69 ) time

Kratsch, D., & Spinrad, J. (2006) · Discrete Mathematics · doi:10.1016/j.disc.2005.12.009 · Cited by 24

A model classifying algorithms as inherently sequential with applications to graph searching

Greenlaw, R. (1992) · Information and Computation · doi:10.1016/0890-5401(92)90033-c · Cited by 20

FFT-like Multiplication of Linear Differential Operators

van der Hoeven, J. (2002) · Journal of Symbolic Computation · doi:10.1006/jsco.2000.0496 · Cited by 20

Steiner Shallow-Light Trees are Exponentially Lighter than Spanning Ones

Elkin, M., & Solomon, S. (2011) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2011.18 · Cited by 20

On graphs without a C 4 or a diamond

Eschen, E. M., Hoàng, C. T., Spinrad, J., & Sritharan, R. (2010) · Discrete Applied Mathematics · doi:10.1016/j.dam.2010.04.015 · Cited by 20

Efficient algorithms for path problems in weighted graphs

Blelloch, G. E., & Williams, V. V. (2008) · Cited by 20

Asymptotic tensor rank of graph tensors: beyond matrix multiplication

Christandl, M., Vrana, P., & Zuiddam, J. (2018) · Computational Complexity · doi:10.1007/s00037-018-0172-8 · Cited by 28

On the partially symmetric rank of tensor products of $W$-states and other symmetric tensors

Ballico, E., Bernardi, A., Christandl, M., & Gesmundo, F. (2019) · Rendiconti Lincei Matematica e Applicazioni · doi:10.4171/rlm/837 · Cited by 20

Fast Structured Matrix Computations: Tensor Rank and Cohn–Umans Method

Ye, K., & Lim, L. (2016) · Foundations of Computational Mathematics · doi:10.1007/s10208-016-9332-x · Cited by 21

All pairs lightest shortest paths

Zwick, U. (1999) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/301250.301271 · Cited by 20

Optimal parallel algorithms for transitive closure and point location in planar structures

Tamassia, R., & Vitter, J. S. (1989) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/72935.72978 · Cited by 20

Recognizing clique graphs of directed and rooted path graphs

Prisner, E., & SZWARCFITER, J. L. (1999) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(99)00028-1 · Cited by 20

Efficient parallel shortest-paths in digraphs with a separator decomposition

Cohen, E. (1993) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/165231.165240 · Cited by 20

A general approach to removing degeneracies

Emiris, I. Z., & Canny, J. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1991.185399 · Cited by 20

Even-hole-free graphs

Silva, D., & Gonçalves, M. V. (2008) · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · Cited by 20

Exact Covers via DeterminantsPreprint

Björklund, A. (2009) · arXiv (Cornell University) · doi:10.4230/lipics.stacs.2010.2447 · Cited by 22

Matchings, matroids and submodular functions

Goemans, M. X., & Harvey, N. J. A. (2008) · Cited by 20

Fast Lowest Common Ancestor Computations in Dags

Eckhardt, S., Mühling, A., & Nowak, J. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-75520-3_62 · Cited by 19

New Approximation Algorithms for Minimum Cycle Bases of Graphs

Kavitha, T., Mehlhorn, K., & Michail, D. (2007) · Springer eBooks · doi:10.1007/978-3-540-70918-3_44 · Cited by 19

Reducing the worst case running times of a family of RNA and CFG problems, using Valiant’s approach

Zakov, S., Tsur, D., & Ziv-Ukelson, M. (2011) · Algorithms for Molecular Biology · doi:10.1186/1748-7188-6-20 · Cited by 19

Randomized preprocessing versus pivoting

Pan, V. Y., Qian, G., & Zheng, A.-L. (2011) · Linear Algebra and its Applications · doi:10.1016/j.laa.2011.02.052 · Cited by 19

Complexity of Finding Graph Roots with Girth Conditions

Farzad, B., Lau, L. C., Lê, V. B., & Tuy, N. N. (2010) · Algorithmica · doi:10.1007/s00453-010-9442-9 · Cited by 19

Perceived Influence and Friendship as Antecedents of Cooperation in Top Management Teams: A Network Approach

Rank, O. N., & Tuschke, A. (2010) · BuR - Business Research · doi:10.1007/bf03342720 · Cited by 21

Approximate shortest path and distance queries in networks

Sommer, C. (2010) · Cited by 19

Optimal 2-constraint satisfaction via sum–product algorithms

Koivisto, M. (2006) · Information Processing Letters · doi:10.1016/j.ipl.2005.11.013 · Cited by 19

Multiplying matrices in O(n 2:373 ) time

Williams, V. V. (2014) · Cited by 19

On Regularity Lemmas and their Algorithmic Applications

Fox, J., LOVÁSZ, L. M., & Zhao, Y. (2017) · Combinatorics Probability Computing · doi:10.1017/s0963548317000049 · Cited by 19

Fast Low-Rank Approximation for Covariance Matrices

Belabbas, M.-A., & Wolfe, P. J. (2007) · IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing · doi:10.1109/camsap.2007.4498023 · Cited by 19

A performance analysis framework for exploiting GPU microarchitectural capability

Zhou, K., Tan, G., Zhang, X., Wang, C., & Sun, N. (2017) · International Conference on Supercomputing · doi:10.1145/3079079.3079083 · Cited by 19

Computing the Girth of a Planar Graph in Linear Time

Chang, H.-C., & Lu, H.-I. (2013) · SIAM Journal on Computing · doi:10.1137/110832033 · Cited by 19

On interval decomposability of 2D persistence modules

Asashiba, H., Buchet, M., Escolar, E. G., Nakashima, K., & Yoshiwaki, M. (2022) · Computational Geometry · doi:10.1016/j.comgeo.2022.101879 · Cited by 33

Point Counting in Families of Hyperelliptic Curves in Characteristic 2

Hubrechts, H. (2007) · LMS Journal of Computation and Mathematics · doi:10.1112/s1461157000001376 · Cited by 19

Algebra and Complexity

Strassen, V. (1994) · Progress in mathematics · doi:10.1007/978-3-0348-9112-7_18 · Cited by 22

Extended dynamic subgraph statistics using h -index parameterized data structures

Eppstein, D., Goodrich, M. T., Strash, D., & Trott, L. (2011) · Theoretical Computer Science · doi:10.1016/j.tcs.2011.11.034 · Cited by 19

Between O ( nm ) and O ( n alpha )

Kratsch, D., & Spinrad, J. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704441435 · Cited by 19

Complexity bounds for the rational Newton-Puiseux algorithm over finite fields

Poteaux, A., & Rybowicz, M. (2011) · Applicable Algebra in Engineering Communication and Computing · doi:10.1007/s00200-011-0144-6 · Cited by 19

On claw-free asteroidal triple-free graphs

Hempel⋆, H., & Kratsch, D. (2002) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(01)00208-6 · Cited by 19

Accelerating Cryptanalysis with the Method of Four Russians.

Bard, G. V. (2006) · Cited by 19

Sparse matrix multiplication and triangle listing in the Congested Clique model

Censor-Hillel, K., Leitersdorf, D., & Turner, E. (2019) · Theoretical Computer Science · doi:10.1016/j.tcs.2019.11.006 · Cited by 27

Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'98

Patarin, J. (2000) · Designs Codes and Cryptography · doi:10.1023/a:1008341625464 · Cited by 19

Finding the Smallest H-Subgraph in Real Weighted Graphs and Related Problems

Williams, V. V., Williams, R., & Yuster, R. (2006) · Lecture notes in computer science · doi:10.1007/11786986_24 · Cited by 19

Representing all minimum spanning trees with applications to counting and generation

Eppstein, D. (1995) · Cited by 19

Finding a heaviest triangle is not harder than matrix multiplication

Czumaj, A., & Andrzej Lingas, B. (2007) · doi:10.82444/warw.33495880 · Cited by 19

Approximating Node Connectivity Problems via Set Covers

Kortsarz, G., & Nutov, Z. (2000) · Lecture notes in computer science · doi:10.1007/3-540-44436-x_20 · Cited by 19

Efficient Detection and Protection of Information in Cross Tabulated Tables I: Linear Invariant Test

Kao, M., & Gusfield, D. (1993) · SIAM Journal on Discrete Mathematics · doi:10.1137/0406037 · Cited by 19

Discrete Green's functions for products of regular graphsPreprint

Ellis, R. B. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0309080 · Cited by 19

Automatic state capture of self-migrating computations in Messengers

Wicke, C., Bic, L., Dillencourt, M. B., & Fukuda, M. (1998) · Lecture notes in computer science · doi:10.1007/bfb0057649 · Cited by 19

Review of "Algebraic Complexity Theory by Peter Bürgisser, Michael Clausen and Amin Shokrollahi", Springer 1997

To, A. W. (2006) · ACM SIGACT News · doi:10.1145/1140612.1140617 · Cited by 19

A connectionist approach for incremental function approximation and on-line tasks

Heinen, M. R. (2011) · Americanae (AECID Library) · Cited by 19

The bulk-synchronous parallel random access machine

Tiskin, A. (1996) · Lecture notes in computer science · doi:10.1007/bfb0024720 · Cited by 18

Improved output-sensitive quantum algorithms for Boolean matrix multiplication

Gall, F. L. (2012) · doi:10.5555/2095116.2095232 · Cited by 18

Target Tracking Using Multiple Patches and Weighted Vector Median Filters

Bins, J., Dihl, L., & Jung, C. R. (2012) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-012-0354-y · Cited by 18

On Parameterized Intractability: Hardness and Completeness

Chen, J., & Meng, J. (2007) · The Computer Journal · doi:10.1093/comjnl/bxm036 · Cited by 18

Robust Low-Complexity MMSE Precoding Algorithm for Cloud Radio Access Networks

Li, N., Fei, Z., Xing, C., Zhu, D., & Lei, M. (2014) · IEEE Communications Letters · doi:10.1109/lcomm.2014.030914.132683 · Cited by 18

Efficient algorithms for maximum weight matchings in general graphs with small edge weights

Huang, C.-C., & Kavitha, T. (2012) · Cited by 18

Empirical Analysis of HPC Using Different Programming Models

Ashraf, M. U., Fouz, F. F., & Eassa, F. E. (2016) · International Journal of Modern Education and Computer Science · doi:10.5815/ijmecs.2016.06.04 · Cited by 18

Three-in-a-tree in near linear time

Lai, K.-Y., Lu, H.-I., & Thorup, M. (2020) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3357713.3384235 · Cited by 18

Cutting multiparticle correlators down to size

Komiske, P., Metodiev, E. M., & Thaler, J. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.036019 · Cited by 24

Computing syzygies in finite dimension using fast linear algebra

Neiger, V., & Schost, É. (2020) · Journal of Complexity · doi:10.1016/j.jco.2020.101502 · Cited by 18

A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping

Cheng, S. L., Argaud, J., Iooss, B., Ponçot, A., & Lucor, D. (2021) · Mathematical Geosciences · doi:10.1007/s11004-021-09951-z · Cited by 18

Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones

Elkin, M., & Solomon, S. (2015) · SIAM Journal on Computing · doi:10.1137/13094791x · Cited by 18

Induced subgraph isomorphism: Are some patterns substantially easier than others?

Floderus, P., Kowaluk, M., Andrzej Lingas, B., & Lundell, E.-M. (2015) · Theoretical Computer Science · doi:10.1016/j.tcs.2015.09.001 · Cited by 18

Fast rectangular matrix multiplication and QR decomposition

Knight, P. A. (1995) · Linear Algebra and its Applications · doi:10.1016/0024-3795(93)00230-w · Cited by 20

A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic

Beliakov, G., & Matiyasevich, Y. (2015) · BIT Numerical Mathematics · doi:10.1007/s10543-015-0547-z · Cited by 19

Efficient enumeration of words in regular languages

Ackerman, M., & Shallit, J. O. (2009) · Theoretical Computer Science · doi:10.1016/j.tcs.2009.03.018 · Cited by 21

FAST MATRIX MULTIPLICATION ALGORITHMS ON MIMD ARCHITECTURES

Dumitrescu, B., Roch, J.-L., & Trystram, D. (1994) · International Journal of Parallel Emergent and Distributed Systems · doi:10.1080/10637199408915454 · Cited by 18

BOUNDED SEARCH TREE ALGORITHMS FOR PARAMETRIZED COGRAPH DELETION: EFFICIENT BRANCHING RULES BY EXPLOITING STRUCTURES OF SPECIAL GRAPH CLASSES

Nastos, J., & Gao, Y. C. (2012) · Discrete Mathematics Algorithms and Applications · doi:10.1142/s1793830912500085 · Cited by 18

A Space and Time Efficient Algorithm for SimRank Computation

Yu, W., Lin, X., & Le, J. (2010) · Asia-Pacific Web Conference · doi:10.1109/apweb.2010.42 · Cited by 18

A note on compressed sensing and the complexity of matrix multiplication

Iwen, M., & Spencer, C. (2009) · Information Processing Letters · doi:10.1016/j.ipl.2009.01.010 · Cited by 18

Fast computation of approximant bases in canonical form

Jeannerod, C.-P., Neiger, V., & Villard, G. (2019) · Journal of Symbolic Computation · doi:10.1016/j.jsc.2019.07.011 · Cited by 18

Abducing Relations in Continuous Spaces

Sato, T., Inoue, K., & Sakama, C. (2018) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2018/270 · Cited by 18

Analyzing the positivity preservation of numerical methods for the Liouville-von Neumann equation

Riesch, M., & Jirauschek, C. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2019.04.006 · Cited by 18

Analyzing Controllability of Bilinear Systems on Symmetric Groups: Mapping Lie Brackets to Permutations

Zhang, W., & Li, J.-S. (2019) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2019.2963164 · Cited by 18

Effective Matrix Methods in Commutative Domains

Malaschonok, G. (2000) · Springer eBooks · doi:10.1007/978-3-662-04166-6_48 · Cited by 18

On the Complexity of Computing Error Bounds

Demmel, J. W., Diament, B., & Malajovich, G. (2001) · Foundations of Computational Mathematics · doi:10.1007/s10208001004 · Cited by 18

Complexity of Deciding Sense of Direction

Boldi, P., & Vigna, S. (2000) · SIAM Journal on Computing · doi:10.1137/s0097539796310801 · Cited by 18

Fast Matrix Multiplication: Limitations of the Laser MethodPreprint

Ambainis, A., Filmus, Y., & Gall, F. L. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1411.5414 · Cited by 19

Qualitative and quantitative information flow analysis for multi-threaded programs

Ngo, T. M. (2014) · doi:10.3990/1.9789036536523 · Cited by 18

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