Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A variant of Ben-Or's lower bound for algebraic decision trees
Information Processing Letters
Lower bounds for algebraic computation trees with integer inputs
SIAM Journal on Computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
A note on center problems with forbidden polyhedra
Operations Research Letters
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In a recent paper Hamacher and Schobel (Oper. Res. Lett. 20 (1997) 165-169) study a minmax location problem in the Euclidean plane that draws its main difficulty from the restriction that the new facility must not be placed within a so-called forbidden region. Hamacher and Schobel derive a polynomial time algorithm for this problem that runs in O(I^3) time for inputs of size I. In this short note we argue that this location problem can be solved in O(IlogI) time by applying standard techniques from computational geometry. Moreover, by providing a matching lower bound in the algebraic computation tree model of computation, we show that the time complexity O(IlogI) is in fact the best possible.