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SYMPHONY requires the use of a third-party callable library (referred to as the LP engine or LP library) to solve the LP relaxations once they are formulated. As with the user functions, SYMPHONY communicates with the LP engine through an API that converts SYMPHONY's internal data structures into those of the LP engine. Currently, the framework will only work with advanced, simplex-based LP engines, such as CPLEX [9], since the LP engine must be able to accept an advanced basis, and provide a variety of data to the framework during the solution process. The internal data structures used for maintaining the LP relaxations are similar to those of CPLEX and matrices are stored in the standard column-ordered format.