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File compression in the case of large files can be time consuming and it is not even necessarily effective. Vast majority of the compression software use algorithms with implementations for CPU architecture. From the beginning of the 2000's the performance of graphic processing units (GPU) have been continuously increasing and at the present time in some cases the GPU exceeds the CPU in performance. However this high performance of the GPU is rarely exploited except in the case of some special tasks such as password cracking or linear algebra calculations. One of the most well-known compression algorithms is the LZO (Lempel-Ziv-Oberhumer). This study discusses the possible ways for the implementation of LZO for GPU Fermi architecture. Three different algorithms are provided and compared and finally it is also shown that the use of GPU can significantly decrease the time of the file compression.