Graded Sparse Graphs and Matroids

Authors

Audrey Lee, University of Massachusetts Amherst
Ileana Streinu, Smith CollegeFollow
Louis Theran, University of Massachusetts Amherst

Document Type

Article

Publication Date

2007

Publication Title

Journal of Universal Computer Science

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.

Keywords

computational geometry, hypergraph, rigidity theory, matroid, pebble game

Volume

13

Issue

11

First Page

1671

Last Page

1679

DOI

dx.doi.org/10.3217/jucs-013-11-1671

ISSN

0948-6968

Rights

© Journal of Universal Computer Science

Comments

Archived as published. Final version archived with publisher's permission.

Recommended Citation

Lee, Audrey; Streinu, Ileana; and Theran, Louis, "Graded Sparse Graphs and Matroids" (2007). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/10