Symmetry and asymmetry, in the context of data compression, refer to the time relation between compression and decompression for a given compression algorithm.
If an algorithm takes the same time to compress a data archive as it does to decompress it, it is considered symmetrical. Note that compression and decompression, even for a symmetric algorithm, may not be perfectly symmetric in practice, depending on the devices the data is being copied to and from, and other factors such as latency and the fragmentation on the device.
In turn, if the compression and decompression times of an algorithm are vastly different, it is considered asymmetrical.
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