Raimund Seidel

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We present a randomized strategy for maintaining balance in dynamically changing search trees that has optimalexpected behavior. In particular, in the expected case a search or an update takes logarithmic time, with the update requiring fewer than two rotations. Moreover, the update time remains logarithmic, even if the cost of a rotation is taken to be(More)
A generalization of the convex hull of a finite set of points in Akl and Toussaint [ 11, for instance, discuss the relevance the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, “o-shapes,” which seem to capture the intuitive of the convex hull problem to pattern recognition. By notions of “fine shape” and(More)
Seidel, R., A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, Computational Geometry: Theory and Applications 1 (1991) 51-64. This paper presents a very simple incremental randomized algorithm for computing the trapezoidal decomposition induced by a set S of n line segments in the(More)
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 found to be on the hull. We also show that this algorithm is asymptotically worst case optimal on a rather realistic model of computation even if the complexity of the(More)
We propose a uniform and general framework for defining and dealing with Voronoi Diagrams. In this framework a Voronoi Diagram is a partition of a domain <italic>D</italic> induced by a finite number of real valued functions on <italic>D</italic>. Valuable insight can be gained when one considers how these real valued functions partition(More)
It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and(More)
An optimal algorithm is presented for constructing an arrangement of hyperplanes in arbitrary dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to improve known worst-case time complexities for five problems: computing all order-k Voronoi diagrams, computing the &#x03BB;-matrix, estimating halfspace(More)
We present two randomized algorithms. One solves linear programs involving m constraints in d variables in expected time O(m). The other constructs convex hulls of n points in Nd, d > 3, in expected time O(nln/2l). In both bounds d is considered to be a constant. In the linear programming algorithm the dependence of the time bound on d is of the form d!.(More)