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- Sergio Cabello, Erin W. Chambers
- SODA
- 2007

We give an <i>O</i>(<i>g</i><sup>2</sup><i>n</i>log <i>n</i>) algorithm to represent the shortest path tree from all the vertices on a single specified face <i>f</i> in a genus <i>g</i> graph. From this representation, any query distance from a vertex in <i>f</i> can be obtained in <i>O</i>(log <i>n</i>) time. The algorithm uses a kinetic data structure,… (More)

- L. Liu, Erin W. Chambers, David Letscher, Tao Ju
- Comput. Graph. Forum
- 2010

Thinning is a commonly used approach for computing skeleton descriptors. Traditional thinning algorithms often have a simple, iterative structure, yet producing skeletons that are overly sensitive to boundary perturbations. We present a novel thinning algorithm, operating on objects represented as cell complexes, that preserves the simplicity of typical… (More)

- Erin W. Chambers, Jeff Erickson, Amir Nayyeri
- Symposium on Computational Geometry
- 2009

We describe the first algorithms to compute minimum cuts in surface-embedded graphs in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s,t)-cut in g<sup>O(g)</sup> n log n time. Except for the special case of planar graphs, for which O(n log… (More)

- Erin W. Chambers, Vin de Silva, Jeff Erickson, Robert Ghrist
- Discrete & Computational Geometry
- 2010

Fix a finite set of points in Euclidean n-space En, thought of as a point-cloud sampling of a certain domain D ⊂ En. The VietorisRips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-computed but high-dimensional approximation to the homotopy type of D. There is a natural “shadow” projection map from the… (More)

- Sergio Cabello, Erin W. Chambers, Jeff Erickson
- SIAM J. Comput.
- 2013

Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time with high probability, so that the shortest-path distance from any vertex on the boundary of f to any other vertex in G… (More)

- Erin W. Chambers, Bill Kinnersley, Noah Prince, Douglas B. West
- SIAM J. Discrete Math.
- 2009

A Roman dominating function of a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑ v∈V (G) f(v) over such functions. Let G be a connected n-vertex graph. We prove that γR(G) ≤ 4n/5, and we characterize the graphs achieving equality. We… (More)

- Erin W. Chambers, Éric Colin de Verdière, Jeff Erickson, Francis Lazarus, Kim Whittlesey
- Comput. Geom.
- 2006

Let <i>M</i> be an orientable combinatorial surface without boundary. A cycle on <i>M</i> is <i>splitting</i> if it has no self-intersections and it partitions <i>M</i> into two components, neither of which is homeomorphic to a disk. In other words, splitting cycles are simple, separating, and non-contractible. We prove that finding the shortest splitting… (More)

- Erin W. Chambers, Jeff Erickson, Pratik Worah
- Symposium on Computational Geometry
- 2008

The (Vietoris-)Rips complex of a discrete point-set <i>P</i> is an abstract simplicial complex in which a subset of <i>P</i> defines a simplex if and only if the diameter of that subset is at most 1. We describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires <i>O</i>(<i>m</i> log… (More)

- Lu Liu, Erin W. Chambers, David Letscher, Tao Ju
- Computer-Aided Design
- 2011

The medial axis is an important shape descriptor first introduced by Blum [2] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a “center… (More)

- Erin W. Chambers, David Letscher
- CCCG
- 2009

Given 2 homotopic curves in a topological space, there are several ways to measure similarity between the curves, including Hausdorff distance and Fréchet distance. In this paper, we examine a different measure of similarity which considers the family of curves represented in the homotopy between the curves, and measures the longest such curve, known as the… (More)