In the last few years, much effort has been devoted to developing join algorithms in order to achieve worst-case optimality for join queries over relational databases. Towards this end, the database community has had considerable success in developing succinct algorithms that achieve worst-case optimal runtime for full join queries, i.e the join is over all variables present in the input database. However, not much is known about join evaluation with {\em projections} beyond some simple techniques of pushing down the projection operator in the query execution plan. Such queries have a large number of applications in entity matching, graph analytics and searching over compressed graphs. In this paper, we study how a class of join queries with projections can be evaluated faster using worst-case optimal algorithms together with matrix multiplication. Crucially, our algorithms are parameterized by the output size of the final result, allowing for choice of the best execution strategy. We implement our algorithms as a subroutine and compare the performance with state-of-the-art techniques to show they can be improved upon by as much as 50x. More importantly, our experiments indicate that matrix multiplication is a useful operation that can help speed up join processing owing to highly optimized open source libraries that are also highly parallelizable.

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