Peer Data Management Systems (PDMS) are a natural extension of heterogeneous database systems. One of the main tasks in such systems is efficient query processing. Insisting on complete answers, however, leads to asking almost every peer in the network. Relaxing these completeness requirements by applying approximate query answering techniques can significantly reduce costs. Since most users are not interested in the exact answers to their queries, rank-aware query operators like top-k or skyline play an important role in query processing. In this paper, we present the novel concept of relaxed skylines that combines the advantages of both rank-aware query operators and approximate query processing techniques. Furthermore, we propose a strategy for processing relaxed skylines in distributed environments that allows for giving guarantees for the completeness of the result using distributed data summaries as routing indexes. Categories and Subject Descriptors H.2.4 [Database Management]:...