Algorithm 1: Cutting of the skyline region based on the convex hull vertices

Input: data node set P, query node set Q

Output: the skyline set S

1: initialize the skyline data table SCH and data access table Visited

2: calculates the CH(Q) by the monitor center

3: for begin with V(p) including some query node q(q2CHv(Q)) and put p into table SCH

4: do traverse Delaunay graph along each edge of CH(Q)

5: if V(p’)(p’2P) is adjacent to V(p) and intersecting with CH(Q) or in CH(Q)

6: then by Theorem 1 and Theorem 3, insert node p into table SCH and table Visited. Issues the current skyline data to those

7: else if V(p’) is adjacent to V(p) and not intersecting with CH(Q) or not in CH(Q)

8: then insert node p’ into table Visited

9: back to the initial data node p

10: end for