Data　integration　techniques　provide　a　communication　bridge　between　isolated　sources　and　offer　a　platform　for　information　exchange.　When　the　schemas　of　heterogeneous　data　sources　map　to　the　centralized　schema　in　a　mediated　data　integration　system　or　a　source　schema　maps　to　a　target　schema　in　a　peer-to-peer　system,　multiple　schema　mappings　may　exist　due　to　the　ambiguities　in　the　attribute　matching.　The　obscure　schema　mappings　lead　to　the　uncertainty　in　query　answering,　and　frequently　people　are　only　interested　in　retrieving　the　best　k　answers　(top-k)　with　the　biggest　probabilities.　Retrieving　the　top-k　answers　efficiently　has　become　a　research　issue.　For　uncertain　queries,　two　semantics,　by-table　and　by-tuple,　have　been　developed　to　capture　top-k　answers　based　on　the　schema　mapping　probabilities.　However,　although　the　existing　algorithms　support　certain　features　to　capture　the　accurate　top-k　answers　and　avoid　accessing　all　data　from　sources,　they　cannot　effectively　reduce　the　number　of　processed　tuples　in　most　cases.　In　this　paper,　new　algorithms　based　on　the　histogram　approximation　and　heuristic　are　proposed　to　efficiently　identify　the　top-k　answers　for　the　data　integration　systems　under　uncertain　schema　mappings.　In　the　experiments,　the　Histogram　algorithm　in　the　by-table　semantics　and　the　expected　approach　in　the　by-tuple　semantics　are　shown　to　significantly　reduce　the　number　of　processed　tuples　while　maintaining　high　accuracy　with　the　estimated　probabilistic　confidence.　©　2018