Download Discrete and Computational Geometry: Japanese Conference, by J. Akiyama, A. Kaneko, M. Kano, G. Nakamura, E. PDF

By J. Akiyama, A. Kaneko, M. Kano, G. Nakamura, E. Rivera-Campo, S. Tokunaga, J. Urrutia (auth.), Jin Akiyama, Mikio Kano, Masatsugu Urabe (eds.)

This quantity comprises these papers offered on the Japan convention on Discrete and Computational Geometry ’98. The convention was once held 9-12 - cember 1998 at Tokai college in Tokyo. with reference to 100 members from 10 nations participated. curiosity in Computational Geometry surfaced between engineers in Japan - out 20 years in the past, whereas curiosity in Discrete Geometry arose as a average extension of the examine of a gaggle of graph theorists extra lately. one of many targets of the convention used to be to compile those teams and to place them involved with specialists in those ?elds from overseas. this is often the second one convention within the sequence. The plan is to carry one each year and to submit the papers of the meetings each years. The organizers thank the sponsors of the convention, particularly, The Institute of academic improvement of Tokai college, Grant-in-Aid of the Ministry of schooling of Japan (A.Saito;(A)10304008), Mitsubishi learn Institute, Sanada Institute of procedure improvement, Japan method, and Upward. in addition they thank specifically T. Asano, D. Avis, V. Chv´ atal, H. Imai, J. Pach, D. R- paport, M. Ruiz, J. O’Rourke, ok. Sugihara, T. Tokuyama, and J. Urrutia for his or her curiosity and support.

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Extra info for Discrete and Computational Geometry: Japanese Conference, JCDCG’98 Tokyo, Japan, December 9-12, 1998. Revised Papers

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Using integer pivoting the number of digits computed can get and remain quite large, increasing the time for basic arithmetic operations. On the other hand, no gcd computations are required. Interestingly the greatest speedups were found to occur with the problems requiring the longest integers. For example, cyclic polytopes required 164 decimal digits in the computation, which ran 18 times faster with integer pivoting than with rational pivoting. Even with integer pivoting, the cost of the the computation using extended precision arithmetic is dominated by the pivot step in the algorithm.

Denote the four parts of S by a, p, y, 6 and hinge a and ,8, p and y, and y and 6. Fix Q and rotate 6, y, p counterclockwise to form the original parallelogram P . 7. It transforms an equilateral triangle to a square. 9. 26 J. Akiyama and G. 8. 9. 1). 1. 1 Every parallelhexagon has a Dudeney dissection to (a) a parallelogram, and (b) a trapezoid. Proof. Let H be a parallelhexagon. Start with a tiling of the plane using H . 2). This will form a Dudeney dissection of H to a parallelogram. 2. (b) Call the vertices of a parallelhexagon tile A , B , C, D, E and F .

Rosenberg, E. Welzl, and D. 274-281, 1982. 7. J. Hagauer and G. Rote: ”Three-Clustering of Points in the Plane,” Proc. 1st Annual European Symp. 192-199, 1993. 8. P. Hansen and B. Jaumard: ”Minimum sum of diameters clustering,” J. 215-226, 1987. 9. A. Hartigan: ”Clustering Algorithms,” John-Wiley, New York, 1975. 46 T. Asano 10. J. 111-118, 1992. 11. J. Hershberger and S. Suri: ”Finding Tailored Partitions,” Proc. of the 5th Annual ACM Symp. 255-265, 1989. 12. M. Inaba, N. Katoh, and H. Imai: ”Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-Clustering,” Proc.

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