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On the shape of a set of points in the plane
- H. Edelsbrunner, D. Kirkpatrick, R. Seidel
- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 1 July 1983
A generalization of the convex hull of a finite set of points in the plane leads to a family of straight-line graphs, "alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets.
Randomized search trees
- R. Seidel, C. Aragon
- Computer Science30th Annual Symposium on Foundations of Computer…
- 30 October 1989
A randomized strategy for maintaining balance in dynamically changing search trees that has optimalexpected behavior, and generalizes naturally to weighted trees, where the expected time bounds for accesses and updates again match the worst-case time bounds of the best deterministic methods.
Constructing arrangements of lines and hyperplanes with applications
- H. Edelsbrunner, J. O'Rourke, R. Seidel
- Mathematics24th Annual Symposium on Foundations of Computer…
- 7 November 1983
An optimal algorithm is presented for constructing an arrangement of hyperplanes in arbitrary dimensions and is shown to improve known worst-case time complexities for five problems: computing all order-k Voronoi diagrams, computing the λ-matrix, estimating halfspace queries, degeneracy testing, and finding the minimum volume simplex determined by a set of points.
On the All-Pairs-Shortest-Path Problem in Unweighted Undirected Graphs
- R. Seidel
- MathematicsJournal of computer and system sciences (Print)
- 1 December 1995
We present an algorithm, APD, that solves the distance version of the all-pairs-shortest-path problem for undirected, unweighted n-vertex graphs in time O(M(n) log n), where M(n) denotes the time…
A Simple and Fast Incremental Randomized Algorithm for Computing Trapezoidal Decompositions and for Triangulating Polygons
- R. Seidel
- Computer ScienceComputational geometry
The Ultimate Planar Convex Hull Algorithm?
We present a new planar convex hull algorithm with worst case time complexity $O(n \log H)$ where $n$ is the size of the input set and $H$ is the size of the output set, i.e. the number of vertices…
Voronoi diagrams and arrangements
It turns out that the standard Euclidean Voronoi diagram of point sets inRd along with its order-k generalizations are intimately related to certain arrangements of hyperplanes, and this fact can be used to obtain new Vor onoi diagram algorithms.
How to net a lot with little: small ε-nets for disks and halfspaces
It is shown that disks and pseudo-disks in the plane as well as halfspaces in R<supscrpt>, which is best possible up to a multiplicative constant, allow-nets of size only &Ogr;(1/1/<italic>ε</italic)), which isbest possibleup to amultiplicative constant.
Small-dimensional linear programming and convex hulls made easy
- R. Seidel
- Computer ScienceDiscrete & Computational Geometry
- 1 August 1991
Two randomized algorithms solve linear programs involvingm constraints ind variables in expected timeO(m) and constructs convex hulls ofn points in ℝd,d>3, in expectedTimeO(n[d/2]).
Constructing higher-dimensional convex hulls at logarithmic cost per face
- R. Seidel
- Computer Science, MathematicsSymposium on the Theory of Computing
- 1 November 1986
The main tool in this new approach is the notion of a straight line shelling of a polytope in convex hull problems, which has best case time complexity O(m 2 -tFlogm), which is an improvement over the best previously achieved bounds for a large range of values of F.