Discrete and Computational Geometry

This volume consists of those papers presented at the Japan Conference on Discrete and Computational Geometry '98. The conference was held 9-12 - cember 1998 at Tokai University in Tokyo. Close to a hundred participants from 10 countries participated. Interest in Computational Geometry surfaced among engineers in Japan - out twenty years ago, while interest in Discrete Geometry arose as a natural extension of the research of a group of graph theorists more recently. One of the goals of the conference was to bring together these two groups and to put them in contact with experts in these ?elds from abroad. This is the second conference in the series. The plan is to hold one every year and to publish the papers of the conferences every two years. The organizers thank the sponsors of the conference, namely, The Institute of Educational Development of Tokai University, Grant-in-Aid of the Ministry of Education of Japan (A.Saito;(A)10304008), Mitsubishi Research Institute, Sanada Institute of System Development, Japan Process, and Upward. They also thank especially T. Asano, D. Avis, V. Chv atal, H. Imai, J. Pach, D. R- paport, M. Ruiz, J. O'Rourke, K. Sugihara, T. Tokuyama, and J. Urrutia for their interest and support.

Inhalt

Papers.- Radial Perfect Partitions of Convex Sets in the Plane.- Dudeney Dissection of Polygons.- Effective Use of Geometric Properties for Clustering.- Living with lrs.- On the Existente of a Point Subset with 4 or 5 Interior Points.- Planar Drawing Algorithms of Survivable Telecommunication Networks.- Polygon Cutting: Revisited.- Algorithms for Packing Two Circles in a Convex Polygon.- Folding and Cutting Paper.- An Interpolant Based on Line Segment Voronoi Diagrams.- 2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces.- NP-Completeness of Stage Illumination Problems.- On the Maximum Degree of Bipartite Embeddings of Trees in the Plane.- Efficient Regular Polygon Dissections.- On Soddy's Hexlet and a Linked 4-Pair.- Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs.- Visibility of Disks on the Lattice Points.- Convex Hull Problem with Imprecise Input.- One-Dimensional Tilings with Congruent Copies of a 3-Point Set.- Polygonal Approximations for Curved Problems: An Application to Arrangements.- Grouping and Querying: A Paradigm to Get Output-Sensitive Algorithms.- Folding and Unfolding in Computational Geometry.- Crossing Numbers.- A Note on the Existente of Plane Spanning Trees of Geometrie Graphs.- Embeddings of Equilateral Polygons in Unit Lattices.- Order-k Voronoi Diagrams, k-Sections, and k-Sets.- "Impossible Objects" Are Not Necessarily Impossible - Mathematical Study on Optical Illusion -.- An Efficient Solution to the Corridor Search Problem.