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Abstract: We describe a general algorithm suitable for executing and coupling components of a software framework on a parallel computer. The requirements of a flexible, efficient and robust algorithm are defined precisely, and the motivation for the requirements is demonstrated on several examples. In short, the requirements are the following: (i) the algorithm should allow arbitrary distribution of processors among the components, (ii) it should allow arbitrary coupling schedule between the components, (iii) it should not use any inter-processor communication other than already required by the components and their couplings, and (iv) it should never get into a dead-lock. We show that the proposed algorithm based on the Temporal and Predefined Ordering of Tasks (TPOT) satisfies all these requirements. The TPOT algorithm has been implemented in the Space Weather Modeling Framework. The flexibility and efficiency of the algorithm is demonstrated with several examples. [Copyright &y& Elsevier]