Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
High-probability parallel transitive closure algorithms
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
On dynamic algorithms for algebraic problems
Journal of Algorithms
Rectangular matrix multiplication revisited
Journal of Complexity
Fast rectangular matrix multiplication and applications
Journal of Complexity
All Algebraic Functions Can Be Computed Fast
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Mathematics for the Analysis of Algorithms
Mathematics for the Analysis of Algorithms
Improved Bounds and New Trade-Offs for Dynamic All Pairs Shortest Paths
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A new approach to dynamic all pairs shortest paths
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fully dynamic biconnectivity and transitive closure
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fully Dynamic All Pairs Shortest Paths with Real Edge Weights
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Dynamic Transitive Closure via Dynamic Matrix Inverse (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for dynamic algebraic problems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Shortest paths in matrix multiplication time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
In this paper we extend a technique introduced in [14] for dynamic matrix functions. We present dynamic algorithms for computing matrix determinant and matrix adjoint over commutative rings. These algorithms are then used to construct an algorithm for dynamic shortest distances in unweighted graph. Our algorithm supports updates in O(n1.932) randomized time and queries in O(n1.288) randomized time. These bound improve over the previous results and solve a long-standing open problem if sub-quadratic dynamic algorithms exist for computing all pairs shortest distances.