By Jin Akiyama, Hiro Ito, Toshinori Sakai

This e-book constitutes the completely refereed post-conference complaints of the sixteenth jap convention on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013.

The overall of sixteen papers incorporated during this quantity used to be conscientiously reviewed and chosen from fifty eight submissions. The papers characteristic advances made within the box of computational geometry and concentrate on rising applied sciences, new technique and purposes, graph concept and dynamics.

**Read or Download Discrete and Computational Geometry and Graphs: 16th Japanese Conference, JCDCGG 2013, Tokyo, Japan, September 17-19, 2013, Revised Selected Papers PDF**

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**Additional resources for Discrete and Computational Geometry and Graphs: 16th Japanese Conference, JCDCGG 2013, Tokyo, Japan, September 17-19, 2013, Revised Selected Papers**

**Example text**

Teach. Math. Appl. 16(3), 95–100 (1997) 4. : Problem 10716: A cubical gift. Am. Math. Monthly 108(1), 81–82 (2001) On Wrapping Spheres and Cubes with Rectangular Paper 43 5. : Wrapping spheres with flat paper. Comput. Geom. Theory Appl. 42(8), 748–757 (2009) 6. : Folding flat silhouettes and wrapping polyhedral packages: New results in computational origami. Comput. Geom. Theory Appl. 16(1), 3–21 (2000) 7. : Geometric Folding Algorithms: Linkages, Origami, Polyhedra, pp. 179–182. Cambridge University Press, New York (2007) 8.

If an R-sphere can be wrapped by an x × 1/x paper, then it can also be wrapped by n congruent disks of diameter x2 + (nx)−2 . Proof. Consider a arbitrary wrapping from an x × 1/x paper to an R-sphere. Partition the ﬂat paper into n small x × 1/(nx) rectangles. Circumscribe each x × 1/(nx) rectangle to get n disks of diameter x2 + (nx)−2 . These disks can contractively map into the original paper. 36 A. Cole et al. g. [8,11]) and for many values of n, bounds exist on how large the diameter d must be to admit a covering of a sphere of radius R.

Theorem 4. There exists an O(n log n)-time 3-approximation algorithm for the opd-tr problem when the input is restricted to non-degenerated components. According to Remarks 1 and 2, we know that Algorithm 1 is able to process not only non-degenerated components but also generic multiple octilinear polygons. This implies that we can provide an approximation result for the opd-tr problem, as follows. Theorem 5. There exists an O(n log n)-time 16-approximation algorithm for the opd-tr problem. 28 S.