In this paper we define a general class of problems in computational geometry that we call connectability problems. Connectability problems involve connecting objects by some kind of connections, avoiding obstacles. This includes many different types of problems like intersection problems, visibility problems, etc. Studying these problems in a general framework might lead to general solutions. Some solutions are presented. In particular, an O(n log nloglog n) solution is given for determining all pairs of points in a set that can be connected with an axis-parallel rectangle, avoiding a set of obstacle points.
KeywordsLine Segment Voronoi Diagram Computational Geometry Priority Queue Left Endpoint
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- de Berg, M.T., and M.H. Overmars, Dominance in the presence of obstacles, Techn. Rep. RUU-CS-88-10, Dept of Computer Science, University of Utrecht, 1988.Google Scholar
- Edelsbrunner, H., and L. Guibas, Topological sweeping in an arrangement, Proc. 18th Symp. Theory of Computing, 1986, pp. 389–403.Google Scholar
- Chew, L.P., and R.L. Drysdale, III, Voronoi diagrams based on convex distance functions, Proc. 1st ACM Symp. Computational Geometry, 1985, pp. 235–244.Google Scholar
- Güting, R.H., O. Nurmi and T. Ottmann, The direct dominance problem, Proc. 1st ACM Symp. Computational Geometry, 1985, pp. 81–88.Google Scholar
- Ghosh, S.K., and D.M. Mount, An output sensitive algorithm for computing visibility graphs, Proc. 28th Symp. on Foundations of Computer Science, 1987, pp. 11–19.Google Scholar
- Karlsson, R.G., and M.H. Overmars, Normalized divide-and-conquer: A scaling technique for solving multi-dimensional problems, Inform. Proc. Lett. 26 (1987/88) pp. 307–312.Google Scholar
- Munro, J.I., M.H. Overmars and D. Wood, Variations on visibility, Proc. 3rd ACM Symp. Computational Geometry, 1987, pp. 291–299.Google Scholar
- Overmars, M.H., and E. Welzl, New methods for computing visibility graphs, Proc. 4th ACM Symp. Computational Geometry, 1988, to appear.Google Scholar
- Overmars, M.H., and D. Wood, On rectangular visibility, J. Algorithms (1988), to appear.Google Scholar
- van Emde Boas, P., Preserving order in a forest in less than logarithmic time and lineair space, Inform. Proc. Lett. 6 (1977) pp. 80–82.Google Scholar
- van Emde Boas, R., R. Kaas and E. Zijlstra, Design and implementation of an efficient priority queue, Math. Systems Theory 10 (1977) pp. 99–127.Google Scholar