This paper presents a new algorithm for skyline computation in database systems, called branch-and-bound skyline (BBS), which is I/O optimal and supports progressive processing. The skyline of a dataset is the set of points not dominated by any other point in all dimensions. Existing algorithms for skyline computation have limitations, such as high I/O costs and inefficiency in progressive processing. BBS is based on nearest-neighbor search and is designed to minimize node accesses, making it more efficient than existing algorithms like NN. BBS is simple to implement and supports various types of progressive processing, including user preferences and arbitrary dimensionality. The paper also proposes several variations of skyline computation and shows how BBS can be applied for their efficient processing. The algorithm is proven to be optimal in terms of node accesses and is efficient in terms of memory consumption. The paper also discusses the incremental maintenance of skylines in the presence of database updates, showing how the skyline can be maintained efficiently when new points are added or removed. The algorithm is evaluated experimentally and is shown to outperform existing algorithms in terms of performance and efficiency.This paper presents a new algorithm for skyline computation in database systems, called branch-and-bound skyline (BBS), which is I/O optimal and supports progressive processing. The skyline of a dataset is the set of points not dominated by any other point in all dimensions. Existing algorithms for skyline computation have limitations, such as high I/O costs and inefficiency in progressive processing. BBS is based on nearest-neighbor search and is designed to minimize node accesses, making it more efficient than existing algorithms like NN. BBS is simple to implement and supports various types of progressive processing, including user preferences and arbitrary dimensionality. The paper also proposes several variations of skyline computation and shows how BBS can be applied for their efficient processing. The algorithm is proven to be optimal in terms of node accesses and is efficient in terms of memory consumption. The paper also discusses the incremental maintenance of skylines in the presence of database updates, showing how the skyline can be maintained efficiently when new points are added or removed. The algorithm is evaluated experimentally and is shown to outperform existing algorithms in terms of performance and efficiency.