Multi-dimensional dynamic facility location and fast computation at query points

Authors:
S. Abravaya;D. Berend
Affiliations:
Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Departments of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
Venue:
Information Processing Letters
Year:
2009

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Abstract

We present O(nlogn) time algorithms for the minimax rectilinear facility location problem in R^1 and R^2. The algorithms enable, once they terminate, computing the cost of any given query point in O(logn) time. Based on these algorithms, we develop a preprocessing procedure which enables solving the following two problems: Fast computation of the cost of any query point in R^d, and fast solution for the dynamic location problem in R^2 (namely, in the presence of an additional facility). Finally, we show that the preprocessing always gives a bound on the optimal value, which allows us in many cases to find the optimum fast (for both the traditional and the dynamic location problems in R^d for any d).