Graph matching, set covering and partitioning problems are both theoretically and practically important in decision support systems. Numerous situations have been modeled as graph matching, set covering and partitioning problems. These situations include applications in the areas of task assignment, marriage problem, airline crew scheduling, truck deliveries or vehicle routing, political redistricting, etc. Relational database systems currently support these applications merely by providing some programming languages which are used to write the programs associated with the data. These programming languages are complete as opposed to existing query languages like SQL. These languages, since they are complete, have the usual complexity of a powerful language and lack the simplicity of query languages. This increases application development effort. Relational operators and the query language SQL are extended in this present work in order to enable these problems to be stated and solved directly by the relational database systems leading to benefits of improved data independence, increased productivity, and better performance. The relational operators are extended with six operators, i.e., match, maxmatch, cover, mincover, partition, and minpartition. Properties of these operators are described. Some of these operators may possibly take a very long time in finding a solution. Genetic algorithms are proposed. These algorithms are bounded by a polynomial time. These algorithms therefore enable DBMS to be capable of responding to queries involving proposed operators in a given time constraint. The database operations and query languages extended in this research provide a powerful tool for users as a database‐query tool which supports some decision support systems for information retrieval from a database.