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Spatial data conflation is aimed at matching and merging objects in two datasets into a more comprehensive one. Starting from the "map assignment problem" in the 1980s, optimized conflation models treat feature matching as a natural optimization problem of minimizing certain metrics, such as the total discrepancy. One complication in optimized conflation is that heterogeneous datasets can represent geographic features differently. Features can correspond to target features in the other dataset either on a one-to-one basis (forming full matches) or on a many-to-one basis (forming partial matches). Traditional models consider either full matching or partial matches exclusively. This dichotomy has several issues. Firstly, full matching models are limited and cannot capture any partial match. Secondly, partial matching models treat full matches just as partial matches, and they are more prone to admit false matches. Thirdly, existing conflation models may introduce conflicting directional matches. This paper presents a new model that captures both full and partial matches simultaneously. This allows us to impose structural constraints differently on full/partial matches and enforce the consistency between directional matches. Experimental results show that the new model outperforms conventional optimized conflation models in terms of precision (89.2%), while achieving a similar recall (93.2%). [ABSTRACT FROM AUTHOR]