With the advent of multicore processors, it has become imperative to write parallel programs if one wishes to exploit the next generation of processors. This paper deals with skyline computation as a case study of parallelizing database operations on multicore architectures. We compare two parallel skyline algorithms: a parallel version of the branch-and-bound algorithm (BBS) and a new parallel algorithm based on skeletal parallel programming. Experimental results show despite its simple design, the new parallel algorithm is comparable to parallel BBS in speed. For sequential skyline computation, the new algorithm far outperforms sequential BBS when the density of skyline tuples is low.