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SciPy 1.0: fundamental algorithms for scientific computing in Python
TLDR
An overview of the capabilities and development practices of SciPy 1.0 is provided and some recent technical developments are highlighted.
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Approximation of the Stability Number of a Graph via Copositive Programming
TLDR
This paper shows how the stability number can be computed as the solution of a conic linear program (LP) over the cone of copositive matrices of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method).
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Author Correction: SciPy 1.0: fundamental algorithms for scientific computing in Python
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
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Reduction of symmetric semidefinite programs using the regular $$\ast$$-representation
TLDR
A general technique to reduce the size ofSemidefinite programming problems on which a permutation group is acting is described, based on a low-order matrix based on the representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices.
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Complexity of semialgebraic proofs
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Complexity of Semi-algebraic Proofs
TLDR
This work constructs polynomial-size bounded degree LSd proofs of the clique-coloring tautologies, the symmetric knapsack problem, and Tseitin's tautology, and proves lower bounds on Lovasz-Schrijver ranks, demonstrating, in particular, their rather limited applicability for proof complexity.
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The Cost of Stability in Coalitional Games
TLDR
A detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings is provided.
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Improved Bounds for the Crossing Numbers of Km, n and Kn
TLDR
Improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values are shown, obtained as a consequence of the new bound on $\Cr(\ksn) 2.1796n^2 - 4.5n".
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On Approximate Graph Colouring and MAX-k-CUT Algorithms Based on the θ-Function
TLDR
This paper shows that the approximation to the chromatic number suggested in De Klerk et al. (2000) is bounded from above by the Lovász θ-function, and suggests a provably good MAX-k-CUT algorithm, and shows that of the algorithm is closely related to that of Frieze and Jerrum.
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Polynomial-time computing over quadratic maps i: sampling in real algebraic sets
TLDR
A procedure that computes, in (dn)O(k) arithmetic operations in D, a set of sampling points in D that intersects nontrivially each connected component of Z that is polynomial-time for constant k.
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