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

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

The forty revised complete papers offered including four invited papers have been rigorously reviewed and chosen from 126 submissions. A extensive number of present facets in algorithmics and knowledge buildings is addressed.

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

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We gratefully acknowledge discussions on the presented topic with Michel Pocchiola, G¨ unter Rote, and Francisco Santos. K. Agarwal, J. J. Guibas, J. Hershberger, L. Zhang. Deformable free space tilings for kinetic collision detection. R. Donald, K. Lynch, D. ), Algorithmic and Computational Robotics: New Directions (Proc. 5th Workshop Algorithmic Found. Robotics), 2001, 83–96. [2] O. Aichholzer, F. Aurenhammer, P. Brass, H. Krasser. Spatial embedding of pseudo-triangulations. Proc. 19th Ann. ACM Sympos.

Vertex-removing flips (as well as edge-removing flips) play an important role for surface realizations of pseudotriangulations in three-space [2]. (a) (b) Fig. 3. Ambiguous geodesics interpretation Remarks. Instead of the vertex-removing flip, a different version – namely the exchanging flip in Figure 3(a) – has been commonly used. It also leads to a valid pseudo-triangulation (which now does contain the vertex v). However, care has to be taken not to misinterpret this version as in Figure 3(b), where the geodesic still lies inside the union of the two pseudo-triangles involved.

We recursively split (P, S) in a balanced way, by applying Theorem 4(2) from Section 5. This constructs a polygonal partition Π of P whose vertex set is S, and where all vertices are pointed. Π is obtained by introducing O(log n) edges internal to P in each Adapting (Pseudo)-Triangulations with a Near-Linear Number of Edge Flips 19 recursive step, and the number of recursive steps is O(log n) as well. By Lemma 4, O(n log2 n) exchanging flips are sufficient to make MPT 1 and MPT 2 contain all the edges of Π.

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