Journal ArticleDOI
Some independence results in complexity theory
Oscar H. Ibarra,Shlomo Moran +1 more
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It is shown, for example, that matrix multiplication is independent of any of the following problems: computing the transitive closure of a graph, the rank of a matrix, a set of independent rows and columns in a Matrix, a maximum bipartite matching, etc.Abstract:
We give a formal definition of a property which informally says that problem B is independent of problem A if the existence of an “oracle” which solves problem A at zero cost does not help to reduce the cost of any algorithm which solves problem B. We then show, for example, that matrix multiplication is independent of any of the following problems: computing the transitive closure of a graph, the rank of a matrix, a set of independent rows and columns in a matrix, a maximum bipartite matching, etc.read more
Citations
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Journal ArticleDOI
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Journal ArticleDOI
A Multi-Criteria Metric Algorithm for Recommender Systems
TL;DR: This paper presents a multi-criteria ranking algorithm that can be used on a non-rigid set of criteria and the system implementing the algorithm fares well with respect to the above qualities.
Book ChapterDOI
Lower Bounds for Algebraic Computation Trees of Functions with Finite Domains
TL;DR: This paper studies the complexity of rational functions and multirational functions, including polynomial functions such as the gcd and modulo of two polynomials.
References
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Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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 ?
Journal ArticleDOI
A generalization of the fast LUP matrix decomposition algorithm and applications
TL;DR: It is shown that any m × n matrix A, over any field, can be written as a product, LSP, of three matrices, where L, S, and P can be found in O(mα−1 n) time, where the complexity of matrix multiplication is O( mα).