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Equation-based modelling is a powerful approach to tame the complexity oflarge-scale simulation problems. Equation-based tools automatically translatemodels into imperative languages. When confronted with nowadays' problems,however, well assessed model translation techniques exhibit scalability issues,that are particularly severe when models contain very large arrays. In fact,such models can be made very compact by enclosing equations into loopingconstructs, but reflecting the same compactness into the translated imperativecode is not trivial. In this paper, we face this issue by concentrating on akey step of equations-to-code translation, the equation/variable matching. Wefirst show that an efficient translation of models with (large) arrays needsawareness of their presence, by defining a figure of merit to measure how muchthe looping constructs are preserved along the translation. We then show thatthe said figure of merit allows to define an optimal array-aware matching, andas our main result, that the so stated optimal array-aware matching problem isNP-complete. As an additional result, we propose a heuristic algorithm capableof performing array-aware matching in polynomial time. The proposed algorithmcan be proficiently used by model translator developers in the implementationof efficient tools for large-scale system simulation.

Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models