  We introduce the problem of Table Reclamation. Given a Source Table and a
large table repository, reclamation finds a set of tables that, when
integrated, reproduce the source table as closely as possible. Unlike query
discovery problems like Query-by-Example or by-Target, Table Reclamation
focuses on reclaiming the data in the Source Table as fully as possible using
real tables that may be incomplete or inconsistent. To do this, we define a new
measure of table similarity, called error-aware instance similarity, to measure
how close a reclaimed table is to a Source Table, a measure grounded in
instance similarity used in data exchange. Our search covers not only
SELECT-PROJECT- JOIN queries, but integration queries with unions, outerjoins,
and the unary operators subsumption and complementation that have been shown to
be important in data integration and fusion. Using reclamation, a data
scientist can understand if any tables in a repository can be used to exactly
reclaim a tuple in the Source. If not, one can understand if this is due to
differences in values or to incompleteness in the data. Our solution, Gen-T,
performs table discovery to retrieve a set of candidate tables from the table
repository, filters these down to a set of originating tables, then integrates
these tables to reclaim the Source as closely as possible. We show that our
solution, while approximate, is accurate, efficient and scalable in the size of
the table repository with experiments on real data lakes containing up to 15K
tables, where the average number of tuples varies from small (web tables) to
extremely large (open data tables) up to 1M tuples.
