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We survey algorithms and hardness results for two important classes of topology optimization problems: computing minimum-weight cycles in a given homotopy or homology class, and computing minimum-weight cycle bases for the fundamental group or various homology groups.

The measure problem of Klee asks for the volume of the union of n axis-parallel boxes in a fixed dimension d. We give an O(n) time algorithm for the special case of all boxes being cubes or, more generally, fat boxes. Previously, the fastest run-time was n 2O(log ∗ , achieved by the general case algorithm of Chan [SoCG 2008]. For the general problem our… (More)

- Jeff Erickson
- 2002

Let Σ be a fixed smooth surface in IR, such that no medial ball touches Σ more than four times, counting with multiplicity, or more than three times at any single point. We show that the Delaunay triangulation of any uniform sample of Σ has complexity O(n logn) in the worst case. We also prove that the Delaunay triangulation of n random points on Σ has… (More)

We construct, for any positive integer n, a family of n congruent convex polyhedra in IR, such that every pair intersects in a common facet. Our polyhedra are Voronoi regions of evenly distributed points on the helix (t, cos t, sin t). The largest previously published example of such a family contains only eight polytopes. With a simple modification, we can… (More)

- Jeff Erickson
- SODA '02
- 2002

The <i>spread</i> of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in IR<sup>3</sup> with spread Δ has complexity O(Δ<sup>3</sup>). This bound is tight in the worst case for all Δ = O(√n). In particular, the Delaunay triangulation… (More)

- Jeff Erickson, Judy E. Scott
- AMCIS
- 2007

Previous research on enterprise resource planning (ERP) systems has focused mainly on the initial implementations of the solution. However, many companies that installed ERP solutions in the late 1990’s are at the point where they need to upgrade their solution to a current release. This paper provides a model that identifies the different types of… (More)

- Jeff Erickson, Jon Brickey
- AMCIS
- 2008

Is it possible to have too much information? This is a question that organizations are trying to address. In today’s information-driven world, organizations have more data than ever to store, access, and retrieve. But how do organizations transform this wealth of information it into a knowledge asset and a strategic advantage? Furthermore, these knowledge… (More)

- Jeff Erickson
- 2014

5 A topological quadrilateral mesh Q of a connected surface in R3 can be extended to a 6 topological hexahedral mesh of the interior domain Ω if and only if Q has an even number 7 of quadrilaterals and no odd cycle in Q bounds a surface inside Ω. Moreover, if such a mesh 8 exists, the required number of hexahedra is within a constant factor of the minimum… (More)

Our final goal here is to present a lower bound on the worst case time complexity of any data structure that solves this problem in the cell probe model of computation. The same idea, together with more careful analysis, can be used to establish a trade-off lower bound for this problem. For a data structure that solves dynamic connectivity (in cell probe… (More)