Fast recognition of pushdown automaton and context-free languages
Information and Control
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
All pairs shortest distances for graphs with small integer length edges
Information and Computation
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
SIAM Journal on Computing
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
Boolean matrix multiplication and transitive closure
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Faster join-projects and sparse matrix multiplications
Proceedings of the 12th International Conference on Database Theory
General context-free recognition in less than cubic time
Journal of Computer and System Sciences
Regularity Lemmas and Combinatorial Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Subcubic Equivalences between Path, Matrix and Triangle Problems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication
Algorithmica - Special Issue: European Symposium on Algorithms, Design and Analysis
SIAM Journal on Computing
Improving quantum query complexity of boolean matrix multiplication using graph collision
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The quantum query complexity of read-many formulas
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n x n Boolean matrices can be computed on a quantum computer in time Õ(n3/2 + nl3/4), where l is the number of non-zero entries in the product, improving over the output-sensitive quantum algorithm by Buhrman and Spalek that runs in [EQUATION] time. This is done by constructing a quantum version of a recent algorithm by Lingas, using quantum techniques such as quantum counting to exploit the sparsity of the output matrix. As far as query complexity is concerned, our results improve over the quantum algorithm by Vassilevska Williams and Williams based on a reduction to the triangle finding problem. One of the main contributions leading to this improvement is the construction of a triangle finding quantum algorithm tailored especially for the tripartite graphs appearing in the reduction.