Mechanisms for resolving a database query are provided. In some instances, these mechanisms include identifying a connected component in a query graph corresponding to the database query. In some instances, these mechanisms further include determining a longest path length for the connected component. In some instances, these mechanisms further include selecting a path having the longest path length. In some instances, these mechanisms still further include building an algebraic expression for the path. In some instances, these mechanisms still further include solving the algebraic expression using matrix-matrix multiplication to provide a solution. And, in some instances, these mechanisms still further include responding to the query based on the solution.