TIGHT QUANTUM BOUNDS FOR COMPUTATIONAL GEOMETRY PROBLEMS
NILTON VOLPATO, ARNALDO MOURA · International Journal of Quantum Information · 2009
We present new quantum lower bounds and upper bounds for several computational geometry problems. The bounds presented here improve on currently known results in a number of ways. We give asymptotically optimal bounds for one of the problems considered, and we provide, up to logarithmic factors, optimal bounds for a number of other problems and, in particular, we settle an open problem of Bahadur et al. Some of these new bounds are obtained using a general algorithm for finding a minimum pair over a given arbitrary order relation.