Computing all large sums-of-pairs in Rn and the discrete planar two-watchtower problem

Authors:
Boaz Ben-Moshe;Paz Carmi;Matthew J. Katz
Affiliations:
Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
Venue:
Information Processing Letters
Year:
2004

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Abstract

We observe that Matousek's algorithm for computing all dominances for a set P of n points in Rn can be employed for computing all pairs of points in such a set whose sum is greater or equal to a given point a ∈ Rn. We apply this observation to the decision problem of the discrete planar two-watchtower problem and obtain an improved solution.