Rigid components in fixed-lattice and cone frameworks
Data Structures and Algorithms
2015-03-19 v1 Combinatorics
Abstract
We study the fundamental algorithmic rigidity problems for generic frameworks periodic with respect to a fixed lattice or a finite-order rotation in the plane. For fixed-lattice frameworks we give an algorithm for deciding generic rigidity and an O(n^3) algorithm for computing rigid components. If the order of rotation is part of the input, we give an O(n^4) algorithm for deciding rigidity; in the case where the rotation's order is 3, a more specialized algorithm solves all the fundamental algorithmic rigidity problems in O(n^2) time.
Cite
@article{arxiv.1105.3234,
title = {Rigid components in fixed-lattice and cone frameworks},
author = {Matthew Berardi and Brent Heeringa and Justin Malestein and Louis Theran},
journal= {arXiv preprint arXiv:1105.3234},
year = {2015}
}