Tracing lineage of array data

Arrays are a common and important class of data in many applications. Arrays can model data such as digital images, digital video, scientific and experimental data, matrices, and finite element grids. Although array manipulations are diverse and domain-specific, they often exhibit structural regularities. This paper describes an algorithm called sub-pushdown to trace data lineage in such array computations. Lineage tracing is a type of data-flow analysis that relates parts of a result array to those parts of the argument (base) arrays that have bearings on the result array parts. Sub-pushdown can be used to trace data lineage in array-manipulating computations expressed in the Array Manipulation Language (AML) that was introduced previously. Sub-pushdown has several useful features. First, the lineage computation is expressed as an AML query. Second, it is not necessary to evaluate the AML lineage query to compute the array data lineage. Third, sub-pushdown never gives false-negative answers. Sub-pushdown has been implemented as part of the ArrayDB prototype array database system that we have built.