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FOCM
2016

Subtraction-Free Complexity, Cluster Transformations, and Spanning Trees

3 years 17 days ago
Subtraction-Free Complexity, Cluster Transformations, and Spanning Trees
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. Contents
Sergey Fomin, Dima Grigoriev, Gleb A. Koshevoy
Added 03 Apr 2016
Updated 03 Apr 2016
Type Journal
Year 2016
Where FOCM
Authors Sergey Fomin, Dima Grigoriev, Gleb A. Koshevoy
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