US Patent 11645278 Complex query evaluation using sideways information passing

A program stored on non-transitory computer-readable storage medium executes a method of evaluating a graph over a query. Decomposition instructions decompose the query into a plurality of subqueries. Evaluation instructions evaluate a subquery of the plurality of subqueries and generate a substitution multiset representing a result of the evaluation of the subquery. Filtration instructions or expansion instructions may operate upon the generated substitution set before passing the substitution set to a next subquery to be evaluated. The filtration instructions identify one or more mappings in the substitution multiset that cannot be safely passed to the second subquery and delete the identified one or more mappings from the substitution multiset. The expansion instructions determine, in a case where the subquery is operated upon by a non-distributive query operator, an expansion of the substitution multiset based at least on adding one or more new substitutions to the substitution multiset.