Recently, a query, called reverse top- \(\varvec{k}\) query, is proposed. The reverse top- \(\varvec{k}\) query takes an object as input and retrieves the users whose top- \(\varvec{k}\) query results include the object while the top- \(\varvec{k}\) query retrieves the top- \(\varvec{k}\) matching objects based on the user preference. In business analysis, reverse top- \(\varvec{k}\) queries are crucial for evaluating product impact and potential market. However, the reverse top- \(\varvec{k}\) query assumes that user’s preference is static. In practice, user preference may change with moods, seasons, economic conditions or other reasons. To overcome this disadvantage, this paper proposes a new reverse top- \(\varvec{k}\) query, named as durable reverse top- \(\varvec{k}\) query, without limitation of user’s preference being static. The durable reverse top- \(\varvec{k}\) query retrieves users who put a given object in the top- \(\varvec{k}\) favorite objects most of the time during a given time period. An efficient pruning-based algorithm for the queries with fixed \(\varvec{k}\) is proposed in this paper. For the case of \(\varvec{k}\) being variable, this paper proposes a pruning-based algorithm with an index to achieve a trade-off between time and space. Experiments on both real and synthetic datasets demonstrate that the proposed algorithms are very efficient.
