Year: 2020
Type: article
Abstract: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graphs: Decision, Spanning, Extraction, Components, Optimization, and Extension. We sketch variations on pebble game algorithms to solve them.
Authors: Audrey Lee, Ileana Streinu, Louis Theran
Institutions: University of Massachusetts Amherst, Smith College
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2963168185