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The problem consists in finding borders in a 2D binary image (where all of the pixels are either 0 or 1). There are several algorithms available for this problem, but most of them are sequential. In a former paper, a parallel border tracking algorithm was proposed. This algorithm was designed to run in Graphics Processing units, and it was based on the sequential algorithm known as the Suzuki algorithm. In this paper, we adapt the previously proposed GPU algorithm so that it can be executed in multicore computers. The resulting algorithm is evaluated against its GPU counterpart. The results show that the performance of the GPU algorithm worsens (or even fails) for very large images or images with many borders. 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