English

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 O(n2)O(n^2) 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.

Keywords

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}
}
R2 v1 2026-06-21T18:08:13.645Z