A quantum search algorithm of two-dimensional convex hull

Cheng Wang,Ri-Gui Zhou

Table 1. The definitions of variables.

Notations Symbol Definition ${\mathop{o}\limits^{\wedge }}_{1},{\mathop{o}\limits^{\wedge }}_{2}$ Convex hull ${O}_{1},{O}_{2}$ Object $S$ Point set $P,{P}^{{\prime} }$ Convex polygon ${P}_{1},{P}_{2},{P}_{3},{P}_{4},{P}_{i}$ Convex hull point $N$ Data size $M$ Solution number $\tilde{N},\tilde{M}$ Sample data size and solutions P(x),$\tilde{P}(x)$ Cumulative distribution function ϵ failure rate ${v}_{0},{v}_{1}$ Coordinate values Convex hull point $k$ A copy to store convex hull point values ${M}_{p}$ The number of convex hull point