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- Jeff Erickson, Kim Whittlesey
- SODA
- 2005

We describe simple greedy algorithms to construct the shortest set of loops that generates either the fundamental group (with a given basepoint) or the first homology group (over any fixed coefficient field) of any oriented 2-manifold. In particular, we show that the shortest set of loops that generate the fundamental group of any oriented combinatorial… (More)

- Jeff Erickson, Sariel Har-Peled
- Symposium on Computational Geometry
- 2002

We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this problem is NP-hard, even for manifolds without boundary and for punctured spheres. We also describe an algorithm with running… (More)

- Pankaj K. Agarwal, Lars Arge, Jeff Erickson
- PODS
- 2000

We propose three indexing schemes for storing a set <italic>S</italic> of <italic>N</italic> points in the plane, each moving along a linear trajectory, so that a query of the following form can be answered quickly: Given a rectangle <italic>R</italic> and a real value <italic>t<subscrpt>q</subscrpt></italic>, report all <italic>K</italic> points of… (More)

- Jeff Erickson
- Discrete & Computational Geometry
- 1996

We establish new lower bounds on the complexity of the following basic geometric problem, attributed to John Hopcroft: Given a set of n points and m hyperplanes in IR, is any point contained in any hyperplane? We de ne a general class of partitioning algorithms, and show that in the worst case, for all m and n, any such algorithm requires time (n logm + nm… (More)

- Jeff Erickson
- SODA
- 1995

We prove an f2(n Ir”l) lower bound for the following problem: For some fixed linear equation in T variables, given a set of n real numbers, do any T of them satisfy th; ecpmtion? Our lower bound holds in a restricted linear decision tree model, in which each decision is based on the sign of an arbitrary afline combination of T or fewer inputs. In this… (More)

- Jeff Erickson
- Symposium on Computational Geometry
- 2001

We consider the complexity of Delaunay triangulations of sets of point s in $\Real^3$ under certain practical geometric constraints. The \emph{spread} of a set of points is the ratio between the longest and shortest pairwise distances. We show that in the worst case, the Delaunay triangulation of $n$ points in~$\Real^3$ with spread $\Delta$ has complexity… (More)

- David Eppstein, Jeff Erickson
- Discrete & Computational Geometry
- 1993

We introduce a new method for nding several types of optimal k-point sets, minimizing perimeter, diameter, circumradius, and related measures, by testing sets of the O(k) nearest neighbors to each point. We argue that this is better in a number of ways than previous algorithms, which were based on high order Voronoi diagrams. Our technique allows us for the… (More)

- Jeff Erickson, Shripad Thite, Fred Rothganger, Jean Ponce
- IEEE Transactions on Robotics
- 2003

This paper addresses the problem of capturing an arbitrary convex object P in the plane with three congruent disc-shaped robots. Given two stationary robots in contact with P, we characterize the set of positions of a third robot, the so-called capture region, that prevent P from escaping to infinity via continuous rigid motion. We show that the computation… (More)

- Jeff Erickson
- SODA
- 2010

We observe that the classical maximum flow problem in any directed planar graph <i>G</i> can be reformulated as a parametric shortest path problem in the oriented dual graph <i>G*</i>. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in <i>O(n</i> log <i>n</i>) time. As we continuously increase the parameter, each… (More)

1 Introduction WC show how to preprocess a set S of points in lRd into an external memory data structure that efficiently supports linear-constraint queries. Each query is in the form of a linear constraint aa x < b; the data structure must report all the points of S that satisfy the constraint. Our goal is to minimize the number of disk blocks required to… (More)