Work

Subtraction-free complexity, cluster transformations, and spanning trees

Year: 2013

Type: article

Abstract: 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.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.1307.8425

Authors: Fomin, Sergey, Grigoriev, Dima, Koshevoy, Gleb

Institutions: University of Michigan, Centre National de la Recherche Scientifique, Central Economics and Mathematics Institute

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2951874353

FWCI: 1.411

Cites: 25

Cited by: 4

Related to: 10