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- Audrey Lee-St. John, Ileana Streinu
- Discrete Mathematics
- 2008

A multi-graph G on n vertices is (k, l)-sparse if every subset of n â‰¤ n vertices spans at most kn âˆ’ l edges. G is tight if, in addition, it has exactly kn âˆ’ l edges. For integer values k and l âˆˆ [0, 2k), we characterize the (k, l)-sparse graphs via a family of simple, elegant and efficient algorithms called the (k, l)-pebble games.

- Audrey Lee-St. John, Ileana Streinu, Louis Theran
- J. UCS
- 2007

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 severalâ€¦ (More)

- Audrey Lee-St. John, Ileana Streinu, Louis Theran
- CCCG
- 2005

We give the first complete analysis that the complexity of finding and maintaining rigid components of planar bar-and-joint frameworks and arbitrary d-dimensional body-and-bar frameworks, using a family of algorithms called pebble games, is O(n). To this end, we introduce a new data structure problem called union pairfind, which maintains disjoint edge setsâ€¦ (More)

- Kirk Haller, Audrey Lee-St. John, Meera Sitharam, Ileana Streinu, Neil White
- Comput. Geom.
- 2009

Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the <i>body-and-cad structure</i>, composed of rigid bodies in 3D constrained by pairwise coincidence, angle and distance constraints. We identify 21 relevant geometric constraints and develop the corresponding infinitesimal rigidity theoryâ€¦ (More)

- Audrey Lee-St. John, Jessica Sidman
- Computer-Aided Design
- 2013

We study the rigidity of body-and-cad frameworks which capture the majority of the geometric constraints used in 3D mechanical engineering CAD software. We present a combinatorial characterization of the generic minimal rigidity of a subset of body-and-cad frameworks in which we treat 20 of the 21 body-and-cad constraints, omitting only point-pointâ€¦ (More)

- Heather Pon-Barry, Becky Wai-Ling Packard, Audrey Lee-St. John
- Computer Science Education
- 2017

A dilemma within computer science departments is developing sustainable ways to expand capacity within introductory computer science courses while remaining committed to inclusive practices. Training near-peer mentors for peer code review is one solution. This paper describes the preparation of near-peer mentors for their role, with a focus on regular,â€¦ (More)

- Audrey Lee-St. John, Ileana Streinu, Louis Theran
- Symposium on Computational Geometry
- 2008

How many pair-wise distances must be prescribed between an unknown set of points, and how should they be distributed, to determine only a discrete set of possible solutions? These questions, and related generalizations, are central in a variety of applications. Combinatorial rigidity shows that in two-dimensions one can get the answer, generically, via anâ€¦ (More)

- James Farre, Helena Kleinschmidt, +4 authors Xilin Yu
- Computer Aided Geometric Design
- 2016

Geometric constraint systems underly popular Computer Aided Design software. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then,â€¦ (More)

- Carlile Lavor, Jon Lee, Audrey Lee-St. John, Leo Liberti, Antonio Mucherino, Maxim Sviridenko
- Optimization Letters
- 2012

Given a weighted, undirected simple graph G = (V,E, d) (where d : E â†’ R+), the Distance Geometry Problem (DGP) is to determine an embedding x : V â†’ R K such that âˆ€{i, j} âˆˆ E â€–xi âˆ’ xjâ€– = dij . Although, in general, the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one suchâ€¦ (More)