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Article Dans Une Revue Foundations of Computational Mathematics Année : 2016

SUBTRACTION-FREE COMPLEXITY, CLUSTER TRANSFORMATIONS, AND SPANNING TREES

Sergey Fomin
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Dima Grigoriev
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Gleb Koshevoy
  • Fonction : Auteur

Résumé

Subtraction-free computational complexity is the version of arithmetic circuit complexity that allows only three operations: addition, multiplication, and division. We use cluster transformations to design efficient subtraction-free algorithms for computing Schur functions and their skew, double, and supersymmetric analogues, thereby generalizing earlier results by P. Koev. We develop such algorithms for computing generating functions of spanning trees, both directed and undirected. A comparison to the lower bound due to M. Jerrum and M. Snir shows that in subtraction-free computations, "division can be exponentially powerful." Finally, we give a simple example where the gap between ordinary and subtraction-free complexity is exponential.
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Dates et versions

hal-03044730 , version 1 (07-12-2020)

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  • HAL Id : hal-03044730 , version 1

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Sergey Fomin, Dima Grigoriev, Gleb Koshevoy. SUBTRACTION-FREE COMPLEXITY, CLUSTER TRANSFORMATIONS, AND SPANNING TREES. Foundations of Computational Mathematics, 2016. ⟨hal-03044730⟩

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