A subexponential algorithm for abstract optimization problems

B. Gartner
1992 Proceedings., 33rd Annual Symposium on Foundations of Computer Science  
An Abstract Optimization Problem (AOP) is a triple (H < ) where H is a nite set, < a total order on 2 H and an oracle that, for given F G H , either reports that F = m i n <fF 0 Gg or returns a set F 0 G with F 0 < F . T o solve the problem means to nd the minimum set in H . W e present a randomized algorithm that solves any A OP with an expected numb e r o f a t m o s t e 2 p n+O( 4 p n ln n) oracle calls, n = jHj. In contrast, any deterministic algorithm needs to make 2 n ; 1 oracle calls in
more » ... 1 oracle calls in the worst case. The algorithm is applied to the problem of nding the minimum distance between two n-vertex (or n-facet) polyhedra in d-space, and to the computation of the smallest ball containing n points in d-space for both problems we give the rst subexponential bounds in d.
doi:10.1109/sfcs.1992.267805 dblp:conf/focs/Gartner92 fatcat:6qccoyc6pnaofde7qowlz6rgna