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Many practical scenarios make it necessary to evaluate top-k queries overdata items with partially unknown values. This paper considers a setting wherethe values are taken from a numerical domain, and where some partial orderconstraints are given over known and unknown values: under these constraints,we assume that all possible worlds are equally likely. Our work is the first topropose a principled scheme to derive the value distributions and expectedvalues of unknown items in this setting, with the goal of computing estimatedtop-k results by interpolating the unknown values from the known ones. We studythe complexity of this general task, and show tight complexity bounds, provingthat the problem is intractable, but can be tractably approximated. We thenconsider the case of tree-shaped partial orders, where we show a constructivePTIME solution. We also compare our problem setting to other top-k definitionson uncertain data.

Top-k Querying of Unknown Values under Order Constraints (Extended Version)