As computer clusters are found to be highly effective for handling massive datasets, the design of efficient parallel algorithms for such a computing model is of great interest. We consider (α, k)-minimal algorithms for such a purpose, where α is the number of rounds in the algorithm, and k is a bound on the deviation from perfect workload balance. We focus on new (α, k)-minimal algorithms for sorting and skew equijoin operations for computer clusters. To the best of our knowledge the proposed sorting and skew join algorithms achieve the best workload balancing guarantee when compared to previous works. Our empirical study shows that they are close to optimal in workload balancing. In particular, our proposed sorting algorithm is around 25% more efficient than the state-of-the-art Terasort algorithm and achieves significantly more even workload distribution by over 50%.