Herbert Edelsbrunner

Algorithms in Combinatorial Geometry

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Topological persistence and simplification

AbstractWe formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.

Optimal point location in a monotone subdivision

Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let

Efficient algorithms for agglomerative hierarchical clustering methods

\mathcal{S}

Combinatorial complexity bounds for arrangements of curves and spheres

denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of m edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in

The union of balls and its dual shape

\mathcal{S}

Topologically sweeping an arrangement

based on separating chains. The new data structure, called a layered dag, can be built in

Hierarchical morse complexes for piecewise linear 2-manifolds

O(m)

Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape

time, uses

Incremental topological flipping works for regular triangulations

O(m)