In some applications of privacy preserving data publishing, a practical demand is to publish a data set on multiple quasi-identifiers for multiple users simultaneously, which poses several challenges. Can we generate one anonymized version of the data so that the privacy preservation requirement like kanonymity is satisfied for all users and the information loss is reduced as much as possible? In this paper, we identify and tackle the novel problem by an elegant solution. The full paper [1] can be found at http://www.cs.sfu. ca/~jpei/publications/butterfly-tr.pdf.