Interpolation by lattice polynomial functions: A polynomial time algorithm [PDF]
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Quentin Brabant +2 more
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Polynomial-time algorithms for submodular Laplacian systems [PDF]
Let $G=(V,E)$ be an undirected graph, $L_G\in \mathbb{R}^{V \times V}$ be the associated Laplacian matrix, and $b \in \mathbb{R}^V$ be a vector. Solving the Laplacian system $L_G x = b$ has numerous applications in theoretical computer science, machine learning, and network analysis.
Kaito Fujii, Tasuku Soma, Yuichi Yoshida
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A Polynomial-Time Algorithm for Outerplanar Diameter Improvement [PDF]
The Outerplanar Diameter Improvement problem asks, given a graph $G$ and an integer $D$, whether it is possible to add edges to $G$ in a way that the resulting graph is outerplanar and has diameter at most $D$. We provide a dynamic programming algorithm that solves this problem in polynomial time.
Nathann Cohen +6 more
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Polynomial-time algorithms for permutation groups [PDF]
A permutation group on n letters may always be represented by a small set of generators, even though its size may be exponential in n. We show that it is practical to use such a representation since many problems such as membership testing, equality testing, and inclusion testing are decidable in polynomial time.
Furst, Merrick +2 more
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Polynomial-time algorithms for quadratic isomorphism of polynomials: The regular case [PDF]
Published in Journal of Complexity, Elsevier, 2015, pp ...
Berthomieu, Jérémy +2 more
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Analysis of Polynomial Time and Non-Polynomial Time of Algorithms
Abstract: The P vs NP problem is one of the most significant open problems in computer science and mathematics. This problem asks whether every problem that can be solved in polynomial time can also be verified in polynomial time. The purpose of this research paper is to explore the P vs NP problem and its relevance in the analysis of algorithms.
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Polynomial time algorithm for solving cyclic games [PDF]
The problem of finding the value and optimal strategies of players in cyclic games is studied. A polynomial time algorithm for solving cyclic games is proposed.
Dmitrii Lozovanu
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On the quantum computational complexity of classical linear dynamics with geometrically local interactions: Dequantization and universality [PDF]
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in simulating ...
Kazuki Sakamoto, Keisuke Fujii
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A max-flow algorithm for positivity of Littlewood-Richardson coefficients [PDF]
Littlewood-Richardson coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the general linear group $\mathrm{GL}(n,\mathbb{C})$.
Peter Bürgisser, Christian Ikenmeyer
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Polynomial Time Algorithms for Bichromatic Problems [PDF]
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear naturally and frequently in the fields like Machine learning, Data mining, and so on, and (ii) we are interested ...
Sayan Bandyapadhyay, Aritra Banik
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