How to multiply matrices faster
How to multiply matrices faster
A Strassen-Newton algorithm for high-speed parallelizable matrix inversion
Proceedings of the 1988 ACM/IEEE conference on Supercomputing
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Efficient parallel algorithms for path problems in directed graphs
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Optimal parallel algorithms for transitive closure and point location in planar structures
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Local reorientation, global order, and planar topology
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Parallel depth-first search in general directed graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The input/output complexity of transitive closure
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
High-probability parallel transitive closure algorithms
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Exploiting fast matrix multiplication within the level 3 BLAS
ACM Transactions on Mathematical Software (TOMS)
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Geometric algorithms for a minimum cost assignment problem
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Mixed-approach algorithms for transitive closure (extended abstract)
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A fast deterministic algorithm for factoring polynomials over finite fields of small characteristic
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
An O(n2) time algorithm for the 2-chain cover problem and related problems
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
A note on checking matrix products (extended abstract)
SAC '92 Proceedings of the 1992 ACM/SIGAPP symposium on Applied computing: technological challenges of the 1990's
Directed s-t numberings, rubber bands, and testing digraph k-vertex connectivity
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Checking approximate computations over the reals
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient computation of Fourier inversion for finite groups
Journal of the ACM (JACM)
Recognizing substrings of LR(k) languages in linear time
ACM Transactions on Programming Languages and Systems (TOPLAS)
Optimally Routing LC Permutations on k-Extra-Stage Cube-Type Networks
IEEE Transactions on Computers
Solving satisfiability and implication problems in database systems
ACM Transactions on Database Systems (TODS)
Computing Popov and Hermite forms of polynomial matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Time-work tradeoffs for parallel algorithms
Journal of the ACM (JACM)
Graph-theoretic methods in database theory
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
An O(n2 algorithm for circular-arc graph recognition
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A scalable parallel Strassen's matrix multiplication algorithm for distributed-memory computers
SAC '95 Proceedings of the 1995 ACM symposium on Applied computing
Finding least common ancestors in directed acyclic graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Fully Dynamic Maintenance of k-Connectivity in Parallel
IEEE Transactions on Parallel and Distributed Systems
Fast context-free grammar parsing requires fast boolean matrix multiplication
Journal of the ACM (JACM)
On computing the diameter of a point set in high dimensional Euclidean space
Theoretical Computer Science
On Single-Fault Set Diagnosability in the PMC Model
IEEE Transactions on Computers
An Improved Algorithm for Implication Testing Involving Arithmetic Inequalities
IEEE Transactions on Knowledge and Data Engineering
Constructing the Spanners of Graphs in Parallel
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
New Applications of the Incompressibility Method
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
On the Power of BFS to Determine a Graphs Diameter
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Proofs Methods for Bisimulation Based Information Flow Security
VMCAI '02 Revised Papers from the Third International Workshop on Verification, Model Checking, and Abstract Interpretation
Bisimulation and Unwinding for Verifying Possibilistic Security Properties
VMCAI 2003 Proceedings of the 4th International Conference on Verification, Model Checking, and Abstract Interpretation
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Fractal Matrix Multiplication: A Case Study on Portability of Cache Performance
WAE '01 Proceedings of the 5th International Workshop on Algorithm Engineering
Estimating All Pairs Shortest Paths in Restricted Graph Families: A Unified Approach
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Bisimulation Algorithms for Stochastic Process Algebras and Their BDD-Based Implementation
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Finding a central vertex in an HHD-free graph
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
An Efficient and Scalable Algorithm for Clustering XML Documents by Structure
IEEE Transactions on Knowledge and Data Engineering
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
TAL recognition in O(M(n2)) time
ACL '95 Proceedings of the 33rd annual meeting on Association for Computational Linguistics
A 2-approximation NC algorithm for connected vertex cover and tree cover
Information Processing Letters
Smith normal form of dense integer matrices fast algorithms into practice
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Learning functions of k relevant variables
Journal of Computer and System Sciences - Special issue: STOC 2003
Processor efficient parallel matching
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Finding large sticks and potatoes in polygons
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
HPCASIA '05 Proceedings of the Eighth International Conference on High-Performance Computing in Asia-Pacific Region
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
On transitive orientations with restricted covering graphs
Information Processing Letters
Polynomial time fragments of XPath with variables
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Graph clustering with network structure indices
Proceedings of the 24th international conference on Machine learning
Adaptive Strassen's matrix multiplication
Proceedings of the 21st annual international conference on Supercomputing
Computing SSA Form with Matrices
Electronic Notes in Theoretical Computer Science (ENTCS)
Faster dynamic matchings and vertex connectivity
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing large matchings fast
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Partitioned probe comparability graphs
Theoretical Computer Science
Using average case intractability in cryptography
AIC'04 Proceedings of the 4th WSEAS International Conference on Applied Informatics and Communications
A (de)constructive approach to program checking
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Finding strongly connected components in parallel using O(log2n) reachability queries
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Functional decomposition of polynomials
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Efficient Secure Linear Algebra in the Presence of Covert or Computationally Unbounded Adversaries
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On the Minimisation of Acyclic Models
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Algebraic Attacks on the Courtois Toy Cipher
Cryptologia
The Mailman algorithm: A note on matrix--vector multiplication
Information Processing Letters
Adaptive Winograd's matrix multiplications
ACM Transactions on Mathematical Software (TOMS)
Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Faster join-projects and sparse matrix multiplications
Proceedings of the 12th International Conference on Database Theory
Theoretical Computer Science
Improved Algorithms for Parsing ESLTAGs: A Grammatical Model Suitable for RNA Pseudoknots
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
DOULION: counting triangles in massive graphs with a coin
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
The Closest Pair Problem under the Hamming Metric
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Parallel Algorithms for Solving Markov Decision Process
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Teaching Public-Key Cryptography in School
ISSEP '10 Proceedings of the 4th International Conference on Informatics in Secondary Schools - Evolution and Perspectives: Teaching Fundamentals Concepts of Informatics
Computing Large Matchings in Planar Graphs with Fixed Minimum Degree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Finding a central vertex in an HHD-free graph
Discrete Applied Mathematics
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Interactive Markov chains: and the quest for quantified quality
Interactive Markov chains: and the quest for quantified quality
Secure linear algebra using linearly recurrent sequences
TCC'07 Proceedings of the 4th conference on Theory of cryptography
A secret sharing scheme using matrices
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
A toolbox for cryptanalysis: linear and affine equivalence algorithms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Faster combinatorial algorithms for determinant and Pfaffian
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Using recursion to boost ATLAS's performance
ISHPC'05/ALPS'06 Proceedings of the 6th international symposium on high-performance computing and 1st international conference on Advanced low power systems
An optimal labeling scheme for workflow provenance using skeleton labels
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Newton's method and FFT trading
Journal of Symbolic Computation
Computing large matchings fast
ACM Transactions on Algorithms (TALG)
New data structures for subgraph connectivity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Clustering coefficient queries on massive dynamic social networks
WAIM'10 Proceedings of the 11th international conference on Web-age information management
Optimized dense matrix multiplication on a many-core architecture
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
Complexity issues for the sandwich homogeneous set problem
Discrete Applied Mathematics
Counting spanning trees in graphs using modular decomposition
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Graph expansion and communication costs of fast matrix multiplication: regular submission
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Computing large matchings in planar graphs with fixed minimum degree
Theoretical Computer Science
SpamWatcher: a streaming social network analytic on the IBM wire-speed processor
Proceedings of the 5th ACM international conference on Distributed event-based system
A deterministic algorithm for the Frieze-Kannan regularity lemma
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the complexity of solving Markov decision problems
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Partitioned probe comparability graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Fast and simple approximation of the diameter and radius of a graph
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Shortest paths in matrix multiplication time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Subquadratic algorithm for dynamic shortest distances
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Colorful triangle counting and a MapReduce implementation
Information Processing Letters
Weighted bipartite matching in matrix multiplication time
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Model checking interactive markov chains
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Communication efficient secure linear algebra
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Verifying persistent security properties
Computer Languages, Systems and Structures
Parallel algorithms for the assignment and minimum-cost flow problems
Operations Research Letters
Operations Research Letters
A note on strategy elimination in bimatrix games
Operations Research Letters
Communication-optimal parallel algorithm for strassen's matrix multiplication
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Graph expansion and communication costs of fast matrix multiplication
Journal of the ACM (JACM)
Budget optimization for online campaigns with positive carryover effects
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Linear regression with random projections
The Journal of Machine Learning Research
PATRIC: a parallel algorithm for counting triangles in massive networks
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Guessing singular dependencies
Journal of Symbolic Computation
A scalable approach to computing representative lowest common ancestor in directed acyclic graphs
Theoretical Computer Science
Effective verification of confidentiality for multi-threaded programs
Journal of Computer Security - Foundational Aspects of Security
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We present a new method for accelerating matrix multiplication asymptotically. This work builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. We make novel use of the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression. Our resulting matrix exponent is 2.376.