A fast expected time algorithm for Boolean matrix multiplication and transitive closure
Patrick O'Neil,Elizabeth O'Neil +1 more
TLDR
A probabilistic algorithm is presented to calculate the Boolean product of two n × n Boolean matrices using an expected number of elementary operations of 0(n2).Abstract:
A probabilistic algorithm is presented to calculate the Boolean product of two n × n Boolean matrices using an expected number of elementary operations of 0(n2). Asymptotically in n, almost all pairs of matrices may be multiplied using this algorithm in 0(n2+e) elementary operations for any e > 0.read more
Citations
More filters
Journal ArticleDOI
Regularity lemmas and combinatorial algorithms
Nikhil Bansal,Ryan Williams +1 more
TL;DR: Improvements on combinatorial methods for CFG parsing, detecting triangle-freeness, and transitive closure are given, and using Weak Regularity, an algorithm for answering queries of the form is S \subseteq V an independent set?
Proceedings ArticleDOI
Regularity Lemmas and Combinatorial Algorithms
Nikhil Bansal,Ryan Williams +1 more
TL;DR: Improvements on combinatorial methods for CFG parsing, detecting triangle-freeness, and transitive closure are given, and using Weak Regularity, an algorithm for answering queries of the form is S \subseteq V an independent set?
Journal ArticleDOI
A Survey of Analysis Techniques for Discrete Algorithms
TL;DR: This survey includes an introduction to the concepts of problem complexity, analysis of algorithms to find bounds on complexity, average-case behavior, and approximation algomthms.
Journal ArticleDOI
An improved transitive closure algorithm
TL;DR: A new, improved algorithm is developed using facts from graph theory and the special properties of Tarjan's algorithm for transitive reduction of a digraph, obtained as a byproduct.
Proceedings ArticleDOI
A suitable algorithm for computing partial transitive closures in databases
TL;DR: It is shown that the algorithm presented uses breadth-first search as its dominant traversal strategy, a graph compression method to minimize temporary results, and Tarjan's technique in a new way to deal with strongly connected components suitable for computing partial transitive closures in databases.
References
More filters
Journal ArticleDOI
Gaussian elimination is not optimal
TL;DR: In this paper, Cook et al. gave an algorithm which computes the coefficients of the product of two square matrices A and B of order n with less than 4. 7 n l°g 7 arithmetical operations (all logarithms in this paper are for base 2).
Proceedings ArticleDOI
Boolean matrix multiplication and transitive closure
TL;DR: A transitive closure method based on matrix inverse is presented which can be used to derive Munro's method and it is shown that his method requires at most O(nα ?