By Bernard Chazelle (auth.), Kyung-Yong Chwa, Oscar H. Ibarra (eds.)
This booklet constitutes the refereed court cases of the ninth overseas Symposium on Algorithms and Computation, ISAAC'98, held in Taejon, Korea, in December 1998.
The forty seven revised complete papers offered have been conscientiously reviewed and chosen from a complete of 102 submissions. The e-book is split in topical sections on computational geometry, complexity, graph drawing, on-line algorithms and scheduling, CAD/CAM and photos, graph algorithms, randomized algorithms, combinatorial difficulties, computational biology, approximation algorithms, and parallel and allotted algorithms.
Read Online or Download Algorithms and Computation: 9th International Symposium, ISAAC’98 Taejon, Korea, December 14–16, 1998 Proceedings PDF
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Additional resources for Algorithms and Computation: 9th International Symposium, ISAAC’98 Taejon, Korea, December 14–16, 1998 Proceedings
Example text
It appears that on a polyhedron, some of the standard properties of furthestsite Voronoi diagrams in the plane no longer hold. For instance, a bisector on the polyhedron is generically a closed curve consisting of as many as Θ(n2 ) straightline segments and/or hyperbolic arcs, in the worst case. In general, it may also contain two-dimensional portions of the surface of the polyhedron. Mount [6] showed that the nearest-neighbor Voronoi diagram of m sites on (the surface of) a polyhedron with n faces with m ≤ n has complexity Θ(n2 ) in the worst case; he also gave an algorithm that computes the diagram in O(n2 log n) time.
Shortest paths on a polyhedron. Internat. J. Comput. Geom. , 6:127–144, 1996. 20 2. D. P. Dobkin and D. G. Kirkpatrick. A linear algorithm for determining the separation of convex polyhedra. J. Algorithms, 6:381–392, 1985. 25 3. D. Leven and Micha Sharir. Intersection and proximity problems and Voronoi diagrams. In J. T. -K. Yap, editors, Advances in Robotics 1: Algorithmic and Geometric Aspects of Robotics, pages 187–228. Lawrence Erlbaum Associates, Hillsdale, NJ, 1987. 22 4. N. Megiddo. Linear-time algorithms for linear programming in R3 and related problems.
2. Next, we compute the region of each site r ∈ Ri in FVD(r ∪ Bl ); to do this, we intersect the regions of r in FVD({r, b}) over all b ∈ Bl . Since Bl has only a constant number of sites, the intersection can be accomplished in O(n2 log n) time for a single red site r ∈ Ri by iterating the intersection procedure in the generic merge step. The time taken for all the sites in Ri is O(|Ri |n2 log n). 3. Next, we compute the region of each site r ∈ Ri in FVD(Ri ∪ Bl ) by intersecting its regions in FVD(r ∪ Bl ) and FVD(Ri ).
