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Heuristic-based methods are among the most popular methods in the process discovery area. This category of methods is composed of two main steps: 1) discovering a dependency graph 2) determining the split/join patterns of the dependency graph. The current dependency graph discovery techniques of heuristic-based methods select the initial set of graph arcs according to dependency measures and then modify the set regarding some criteria. This can lead to selecting the non-optimal set of arcs. Also, the modifications can result in modeling rare behaviors and, consequently, low precision and non-simple process models. Thus, constructing dependency graphs through selecting the optimal set of arcs has a high potential for improving graphs quality. Hence, this paper proposes a new integer linear programming model that determines the optimal set of graph arcs regarding dependency measures. Simultaneously, the proposed method can eliminate some other issues that the existing methods cannot handle completely; i.e., even in the presence of loops, it guarantees that all tasks are on a path from the initial to the final tasks. This approach also allows utilizing domain knowledge by introducing appropriate constraints, which can be a practical advantage in real-world problems. To assess the results, we modified two existing methods of evaluating process models to make them capable of measuring the quality of dependency graphs. According to assessments, the outputs of the proposed method are superior to the outputs of the most prominent dependency graph discovery methods in terms of fitness, precision, and especially simplicity.