In this paper, we design and implement a variety of parallel algorithms for both sweep spin selection and random spin selection. We analyze our parallel algorithms on LogP, a portable and general parallel machine model. We then obtain rigorous theoretical runtime results on LogP for all the parallel algorithms. Moreover, a guiding equation is derived for choosing data layouts (blocked vs. stripped) for sweep spin selection. In regard to random spin selection, we are able to develop parallel algorithms with efficient communication schemes. We introduce two novel schemes, namely the FML scheme and the α-scheme. We analyze randomness of our schemes using statistical methods and provide comparisons between the different schemes.