The skyline query and its variant queries are useful functions in the early stages of a knowledge-discovery processes. The skyline query and its variant queries select a set of important objects, which are better than other common objects in the dataset. In order to handle big data, such knowledge-discovery queries must be computed in parallel distributed environments. In this paper, we consider an efficient parallel algorithm for the "K-skyband query" and the "top-k dominating query", which are popular variants of skyline query. We propose a method for computing both queries simultaneously in a parallel distributed framework called MapReduce, which is a popular framework for processing "big data" problems. Our extensive evaluation results validate the effectiveness and efficiency of the proposed algorithm on both real and synthetic datasets.