Non-abelian analogs of lattice rounding

Author:

Begelfor Evgeni,Miller Stephen D.,Venkatesan Ramarathnam

Abstract

AbstractLattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we consider an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out

Funder

NSF

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Computer Networks and Communications

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