  Join operations (especially n-way, many-to-many joins) are known to be time-
and resource-consuming. At large scales, with respect to table and join-result
sizes, current state of the art approaches (including both binary-join plans
which use Nested-loop/Hash/Sort-merge Join algorithms or, alternatively,
worst-case optimal join algorithms (WOJAs)), may even fail to produce any
answer given reasonable resource and time constraints. In this work, we
introduce a new approach for n-way equi-join processing, the Graphical Join
(GJ). The key idea is two-fold: First, to map the physical join computation
problem to PGMs and introduce tweaked inference algorithms which can compute a
Run-Length Encoding (RLE) based join-result summary, entailing all statistics
necessary to materialize the join result. Second, and most importantly, to show
that a join algorithm, like GJ, which produces the above join-result summary
and then desummarizes it, can introduce large performance benefits in time and
space. Comprehensive experimentation is undertaken with join queries from the
JOB, TPCDS, and lastFM datasets, comparing GJ against PostgresQL and MonetDB
and a state of the art WOJA implemented within the Umbra system. The results
for in-memory join computation show performance improvements up to 64X, 388X,
and 6X faster than PostgreSQL, MonetDB and Umbra, respectively. For on-disk
join computation, GJ is faster than PostgreSQL, MonetDB and Umbra by up to
820X, 717X and 165X, respectively. Furthermore, GJ space needs are up to
21,488X, 38,333X, and 78,750X smaller than PostgresQL, MonetDB, and Umbra,
respectively.
