Download Algorithms and Computation: 9th International Symposium, by Bernard Chazelle (auth.), Kyung-Yong Chwa, Oscar H. Ibarra PDF

By Bernard Chazelle (auth.), Kyung-Yong Chwa, Oscar H. Ibarra (eds.)

This booklet constitutes the refereed complaints of the ninth foreign Symposium on Algorithms and Computation, ISAAC'98, held in Taejon, Korea, in December 1998.
The forty seven revised complete papers provided have been rigorously 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 snap shots, graph algorithms, randomized algorithms, combinatorial difficulties, computational biology, approximation algorithms, and parallel and disbursed algorithms.

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Extra info for Algorithms and Computation: 9th International Symposium, ISAAC’98 Taejon, Korea, December 14–16, 1998 Proceedings

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New results and methods. This paper gives an O(mn2 log2 m(log m + log n)) time algorithm to compute the furthest-site Voronoi diagram and find the facility center for a set S of m sites on the surface of a polyhedron with n faces. Given the linear-time algorithm for finding the facility center in the plane, this bound may seem disappointing. However, the algorithm for computing the furthest-site Voronoi diagram is near-optimal, as the maximum combinatorial complexity of the diagram is Θ(mn2 ). 2 Geometric Preliminaries Previous papers on shortest paths on polyhedra [8,5,1,9] use a number of important concepts that we’ll need as well.

The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the optimum placement, we compute the furthest-site Voronoi diagram of the sites on the polyhedron. The diagram has maximum combinatorial complexity Θ(mn2 ), and the algorithm runs in O(mn2 log2 m(log m + log n)) time. 1 Introduction Problem statement. A (polyhedral) terrain is the graph of a piecewise-linear function defined over a simply-connected subset of the plane.

The region of r in FVD(Ri ∪ Bj+1 ) contains all points that are further from r than from any other site in Ri ∪ Bj+1 , and the region of r in FVD(Ri+1 ∪ Bj ) contains all points that are further from r than from any other site in Ri+1 ∪ Bj . The region of r in FVD(Ri ∪ Bj ) is therefore the intersection of its regions in FVD(Ri ∪ Bj+1 ) and FVD(Ri+1 ∪ Bj ). We can compute this intersection for each face of the polyhedron separately by a line-sweep of the regions of r in FVD(Ri ∪ Bj+1 ) and FVD(Ri+1 ∪ Bj ).

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