Paper list

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Pick your paper below. Papers that have been claimed will be crossed out.

1. L. Valiant. General context-free recognition in less than cubic time, JCSS 1975. (Trey) [pdf]
   Description: Valiant shows how to use fast Boolean matrix multiplication to do context free grammar parsing.
   
   
2. L. Lee. Fast Context-Free Parsing Requires Fast Boolean Matrix Multiplication, JACM 2002. (Nicole) [pdf]
   Description: Lee shows that context free grammar parsing requires Boolean matrix multiplication, i.e. that any subcubic algorithm for it implies a subcubic algorithm for BMM.
   
   
3. Amir Abboud, Arturs Backurs, V.V.Williams. If the Current Clique Algorithms are Optimal, so is Valiant’s Parser, FOCS'15. (Colin) [pdf]
   Description: We give a new reduction to CFG parsing from k-Clique, showing that improving upon Valiant's parser even for constant size CFGs would imply new algorithms for k-Clique. This improves upon Lee's result, but making a different assumption.
   
   
4. N. Bansal, R. Williams. Regularity Lemmas and Combinatorial Algorithms. Theory of Computing 2012. (Andrea) [pdf]
   Description: Bansal and Williams show that by using graph regularity one can improve upon the Four-Russians algorithm for BMM.
   
   
5. Huacheng Yu. An improved combinatorial algorithm for Boolean Matrix Multiplication, ICALP'15. (Alex A.) [pdf]
   Description: Yu improves upon Bansal and Williams' result, and a follow-up result by Chan, and gives an O(n^3/log^4 n) algorithm for BMM.
   
   
6. A. Czumaj and A. Lingas. Finding a Heaviest Vertex-Weighted Triangle Is not Harder than Matrix Multiplication. SIAM J. Comput. 2009. (Arun) [pdf]
   Description: The authors show how one can find a min weight triangle in a node-weighted graph in matrix-multiplication time.
   
   
7. P. Vaidya. Speeding-Up Linear Programming Using Fast Matrix Multiplication, FOCS 1989. (Andrew L.) [pdf]
   Description: The author gives an algorithm for linear programming based on matrix multiplication.
   
   
8. R. Duan and S. Pettie. Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths, SODA 2009. (Will M.) [pdf]
   Description: The authors improve upon the first subcubic algorithm for bottleneck paths, obtaining the currently fastest algorithm for the problem.
   
   
9. T. Takaoka, Efficient Algorithms for the Maximum Subarray Problem by Distance Matrix Multiplication, CATS 2002. (Cynthia) [pdf]
   Description: The author presents an algorithm for the Max Subarray problem using APSP.
   
   
10. H. Gabow, P. Sankowski. Algebraic Algorithms for b-Matching, Shortest Undirected Paths, and f-Factors, FOCS 2013. (Kathy) [pdf]
    Description: The authors present algorithms for shortest paths in undirected graphs with possibly negative weights, for b-matching and max flow, all based on matrix multiplication.
    
    
11. R. Yuster and U. Zwick, Fast sparse matrix multiplication, TALG 2005. (Arjun) [pdf]
    Description: The authors present a fast algorithm for sparse matrix multiplication using fast dense matrix multiplication and bucketting.
    
    
12. H. Cohn, R. Kleinberg, B. Szegedy, C. Umans, Group-theoretic Algorithms for Matrix Multiplication, FOCS 2005. (Ilan) [pdf]
    Description: The authors propose a new approach to matrix multiplication based on finding groups with special properties.
    
    
13. N. Alon, A. Shpilka, C. Umans, On sunflowers and matrix multiplication, CCC 2012. (Bill) [pdf]
    Description: The authors prove interesting connections between a conjecture in combinatorics and conjectures about matrix multiplication algorithms.
    
    
14. X. Huang, V. Pan. Fast Rectangular Matrix Multiplication and Applications. J. Complexity 1998. [pdf]
    Description: The authors present bounds for multiplying rectangular matrices. These bounds were not improved for several decades.
    
    
15. D. Coppersmith, Rapid Multiplication of Rectangular Matrices, SIAM J. Comput. 1982. (Han) [pdf]
    Description: The author gives two proofs that there is some constant a>0.1 for which one can multiply n x n^a by n^a x n matrices in essentially optimal O~(n^2) time.
    
    
16. F. Le Gall. Faster Algorithms for Rectangular Matrix Multiplication, FOCS 2012. [pdf]
    Description: The author improves upon the longstanding bounds of Huang and Pan. His improvement implies for instance that Zwick's APSP algorithm runs in O(n^{2.532}) time.
    
    
17. M. Kowaluk, A. Lingas, E. Lundell. Counting and Detecting Small Subgraphs via Equations, SIAM J. Discrete Math. 2013. (Nolan) [pdf]
    Description: The authors present a framework for counting small pattern subgraphs using matrix multiplication.
    
    
18. V.V.Williams, Josh Wang, Ryan Williams and Huacheng Yu. Finding Four-node subgraphs in triangle time, SODA'15. (Vaggos) [pdf]
    Description: This paper shows how to detect any 4-node induced subgraph in the same time as finding a triangle, using matrix multiplication.
    
    
19. Andreas Bjorklund, Rasmus Pagh, V.V. Williams, Uri Zwick. Listing Triangles, ICALP'14. (Ron) [pdf]
    Description: This paper has the current best algorithm for listing triangles in a given graph. They use matrix multiplication.
    
    
20. Greg Valiant, Finding Correlations in Subquadratic Time, with Applications to Learning Parities and the Closest Pair Problem, FOCS'12. (Vatsal) [pdf]
    Description: This paper uses matrix multiplication to find two correlated vectors that are hidden among a set of random vectors.
    
    
21. Don Coppersmith, Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm, Mathematics of Computation, 1994. (Brad) [pdf]
    Description: Coppersmith gives a space-efficient algorithm for solving large sparse systems of homogenous linear equations over GF(2).