Jeff Erickson

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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)
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 &#916; has complexity O(&#916;<sup>3</sup>). This bound is tight in the worst case for all &#916; = O(&radic;n). In particular, the Delaunay triangulation(More)
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)
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)