Abstract Due to the growth of the 3D technology, digital 3D models represented in the form of point clouds have attracted a lot of attention from both industry and academia. In this paper, due to a variety of applications, we study a fundamental problem called the 3D object retrieval, which is to find a set of 3D point clouds stored in a database that are similar to a given query 3D point cloud. To the best of our knowledge, solving the problem of 3D object retrieval efficiently remains unexplored in the research community. In this paper, we propose a framework called C $$_2$$ 2 O to find the answer efficiently with the help of an index built on the database. In most of our experiments, C $$_2$$ 2 O performs up to 2 orders of magnitude faster than all adapted algorithms in the literature. In particular, when the database size scales up to 100 million points, C $$_2$$ 2 O answers the 3D object retrieval within 10 s but all adapted exact algorithms need more than 1000 s.

The traditional top-k query was proposed to obtain a small subset from the database according to the user preference, which is explicitly expressed as a ranking scheme (i.e., utility function). However, a poorly-designed utility function may create discrimination, which in turn may cause harm to minority groups, e.g., women and ethnic minorities, and thus, fairness is becoming increasingly important in many situations, e.g., hiring and admission decisions. Motivated by this, we study fair ranking to alleviate discrimination. We design a fairness model, called α-fairness, to quantify the fairness of utility functions. We propose an efficient exact framework with a basic implementation and an improved implementation to find the fairest utility function with the minimum modification penalty. We conducted extensive experiments on both real and synthetic datasets to demonstrate our effectiveness and efficiency compared with the prior studies.