Homology Flows, Cohomology Cuts ∗ (2009)
Erin W. Chambers, Jeff Erickson, Amir Nayyeri, John Dryden, All For Love, Erin Chambers, ...
We describe the first algorithms to compute maximum flows in surface-embedded graphs in nearlinear time. Specifically, given an undirected graph embedded on an orientable surface of genus g, with two...
Walking Your Dog in the Woods in Polynomial Time (2008)
Erin W. Chambers, Éric Colin, Verdière Jeff, Erickson Sylvain Lazard, Francis Lazarus, Shripad Thite
Given two input curves, the Fréchet distance, sometimes called the dog-leash distance, between them is defined as the minimum length of a leash required to connect a dog and its owner as they walk...
Erin W. Chambers, Daniel Cranston, Kevin Milans
Abstract Given a distribution of pebbles on the vertices of a graph G, a pebbling move takes two pebbles from one vertex and puts one on a neighboring vertex. The pebbling number \Pi (G) is the...
ABSTRACT Splitting (Complicated) Surfaces Is Hard ∗ (2008)
Erin W. Chambers, Francis Lazarus, Jeff Erickson, Kim Whittlesey
Let M be an orientable combinatorial surface without boundary. A cycle on M is splitting if it has no self-intersections and it partitions M into two components, neither of which is homeomorphic to a...
Testing Contractibility in Planar Rips Complexes ∗ (2008)
Erin W. Chambers, Jeff Erickson, Pratik Worah
The (Vietoris-)Rips complex of a discrete point-set P is an abstract simplicial complex in which a subset of P defines a simplex if and only if the diameter of that subset is at most 1. We describe...
Rips Complexes of Planar Point Sets (2007)
Chambers, Erin W., De Silva, Vin, Erickson, Jeff, Ghrist, Robert
Fix a finite set of points in Euclidean $n$-space $\euc^n$, thought of as a point-cloud sampling of a certain domain $D\subset\euc^n$. The Rips complex is a combinatorial simplicial complex based on...
Rips complexes of planar point sets (2007)
Erin W. Chambers, Vin De Silva, Jeff Erickson, Robert Ghrist
ABSTRACT. Fix a finite set of points in Euclidean n-space E n, thought of as a point-cloud sampling of a certain domain D ⊂ E n. The Rips complex is a combinatorial simplicial complex based on...
Rips complexes of planar point sets (2007)
Erin W. Chambers, Vin De Silva, Jeff Erickson, Robert Ghrist
ABSTRACT. Fix a finite set of points in Euclidean n-space E n, thought of as a point-cloud sampling of a certain domain D ⊂ E n. The Rips complex is a combinatorial simplicial complex based on...
Splitting (complicated) surfaces is hard (2006)
Erin W. Chambers, Éric Colin, Verdière Jeff, Erickson Francis, Lazarus Kim Whittlesey
Let M be an orientable surface without boundary. A cycle on M is splitting if it has no self-intersections and it partitions M into two components, neither homeomorphic to a disk. In other words,...
Splitting (complicated) surfaces is hard (2006)
Erin W. Chambers, Éric Colin, Verdière Jeff Erickson, Francis Lazarus, Kim Whittlesey
Let M be an orientable surface without boundary. A cycle on M is splitting if it has no self-intersections and it partitions M into two components, neither homeomorphic to a disk. In other words,...