The Jagiellonian-PET (J-PET) collaboration is developing a prototype TOF-PET detector based on long polymer scintillators. This novel approach exploits the excellent time properties of the plastic scintillators, which permit very precise time measurements. The very fast, FPGA-based front-end electronics and the data acquisition system, as well as, low- and high-level reconstruction algorithms were specially developed to be used with the J-PET scanner. The TOF-PET data processing and reconstruction are time and resource demanding operations, especially in case of a large acceptance detector, which works in triggerless data acquisition mode. In this article, we discuss the parallel computing methods applied to optimize the data processing for the J-PET detector. We begin with general concepts of parallel computing and then we discuss several applications of those techniques in the J-PET data processing.