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The increase in the use of parallel distributed architectures in order to solve large-scale scientific problems has generated the need for performance prediction for both deterministic applications and non-deterministic applications. The development of a new prediction methodology to estimate the execution time of a hard data-dependent parallel application that solves the traveling salesman problem (TSP) is the primary target of this study. The prediction methodology is an analytical process designed to explore a group of cities in search of patterns and/or relationships between these cities, and then to validate performance prediction for new cities sets by applying the detected patterns. The TSP problem is of considerable importance not only from a theoretical point of view. There are important cases of practical problems that can be formulated as TSP problems and many other problems are generalizations of this problem. Therefore, there is a tremendous need for TSP algorithms and still more for knowing their performance values. Three different parallel algorithms of the Euclidean TSP are used to apply the proposed methodology. The experimental results are quite promising; the capacity of prediction is greater than 75%.