We introduce approximate query techniques for searching and analyzing two-dimensional data sets such as line or scatter plots. Our techniques allow users to explore a dataset by defining QueryLines: soft constraints and preferences for selecting and sorting a subset of the data. By using both preferences and soft constraints for query composition, we allow greater flexibility and expressiveness than previous visual query systems. When the user over-constrains a query, for example, a system using approximate techniques can display ?near misses?to enable users to quickly and continuously refine queries. CHI 2005 This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an a...