Facility Location on Terrains

Authors:
Boris Aronov;Marc J. van Kreveld;René van Oostrum;Kasturi R. Varadarajan
Affiliations:
-;-;-;-
Venue:
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Year:
1998

Citing 3
Cited 2

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Computing an approximation of the 1-center problem on weighted terrain surfaces

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Abstract

Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. 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(logm + log n)) time.