Computation of matrix chain products. Part II
SIAM Journal on Computing
How to multiply matrices faster
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Journal of the ACM (JACM)
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SIAM Journal on Computing
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Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
ACM Transactions on Mathematical Software (TOMS)
An O(n) algorithm for determining a near-optimal computation order of matrix chain products
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Introduction to Algorithms
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Information Processing Letters
Lower Bounds for Matrix Product
SIAM Journal on Computing
On the Complexity of Matrix Product
SIAM Journal on Computing
A Group-Theoretic Approach to Fast Matrix Multiplication
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algebraic Complexity Theory
All-pairs bottleneck paths for general graphs in truly sub-cubic time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster join-projects and sparse matrix multiplications
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WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Dynamic plane transitive closure
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Generating a d-dimensional linear subspace efficiently
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Better size estimation for sparse matrix products
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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The VLDB Journal — The International Journal on Very Large Data Bases
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
Compressed matrix multiplication
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Space-round tradeoffs for MapReduce computations
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All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
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Compressed matrix multiplication
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
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ACM Transactions on Knowledge Discovery from Data (TKDD)
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Let A and B two n×n matrices over a ring R (e.g., the reals or the integers) each containing at most m nonzero elements. We present a new algorithm that multiplies A and B using O(m0.7n1.2+n2+o(1)) algebraic operations (i.e., multiplications, additions and subtractions) over R. The naïve matrix multiplication algorithm, on the other hand, may need to perform Ω(mn) operations to accomplish the same task. For m≤n1.14, the new algorithm performs an almost optimal number of only n2+o(1) operations. For m≤n1.68, the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses O(n2.38) algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast rectangular matrix multiplication algorithms. We also obtain improved algorithms for the multiplication of more than two sparse matrices. As the known fast rectangular matrix multiplication algorithms are far from being practical, our result, at least for now, is only of theoretical value.