Algorithms and Data Structures: 8th International Workshop, by Gilles Brassard, Anne Broadbent, Alain Tapp (auth.), Frank

By Gilles Brassard, Anne Broadbent, Alain Tapp (auth.), Frank Dehne, Jörg-Rüdiger Sack, Michiel Smid (eds.)

This booklet constitutes the refereed court cases of the eighth overseas Workshop on Algorithms and knowledge constructions, WADS 2003, held in Ottawa, Ontario, Canada, in July/August 2003.

The forty revised complete papers awarded including four invited papers have been rigorously reviewed and chosen from 126 submissions. A vast number of present elements in algorithmics and information buildings is addressed.

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Extra resources for Algorithms and Data Structures: 8th International Workshop, WADS 2003, Ottawa, Ontario, Canada, July 30 - August 1, 2003. Proceedings

Example text

The existence of MPT is given by Theorem 3. The O(log n) edges of ∇ that are used to partition (P, S) retain the pointedness of all vertices, as do the two segments from Lemma 6 that may have to be used to split ∇. Remarks. The fraction 23 in Lemma 6 is optimal, even if ∇ is a triangle. The set M may consist of three groups of 3i points such that, for each choice of p ∈ M , the two groups not containing p end up in the same subset. Theorem 4 is similar in flavor to a result in [9], which asserts that any simple n-gon can be split by a diagonal into two subpolygons with at most 23 n vertices.

Minima always have index 0 and maxima always have index d. The driver of a point in Rd can now also be described in terms of Voronoi- and Delaunay objects. Lemma 3. Given x ∈ Rd . Let V be the lowest dimensional Voronoi object in the Voronoi diagram of P that contains x and let σ be the dual Delaunay object of V . The driver of x is the point on σ closest to x. We have a much more explicit characterization of the flow induced by a finite point set than in the general case. Observation 2 The flow φ induced by a finite point set P is given as follows.

The Voronoi cell of p ∈ P is given as Vp = {x ∈ Rd : ∀q ∈ P − {p}, x − p ≤ x − q )}. The sets Vp are convex polyhedra or empty since the set of points that have the same distance from two points in P forms a hyperplane. Closed facets shared by k, 2 ≤ k ≤ d, Voronoi cells are called (d − k + 1)-dimensional Voronoi facets and points shared by d + 1 or more Voronoi cells are called Voronoi vertices. The term Voronoi object denotes either a Voronoi cell, facet, edge or vertex. The Voronoi diagram VP of P is the collection of all Voronoi objects.

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